http://www.physicsbook.gatech.edu/api.php?action=feedcontributions&feedformat=atom&user=MmcdanielPhysics Book - User contributions [en]2026-05-04T03:46:15ZUser contributionsMediaWiki 1.42.7http://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=14162Simple Harmonic Motion2015-12-05T14:51:57Z<p>Mmcdaniel: /* Simple */</p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=Acos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2π/ω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
Problem: A spring has a restoring force of 300 N when it is stretched -.2m. What is the spring's constant <math>{K_{s}}</math>. in N/m? <br />
<br />
Solution:<math>F={-K_{s}}*s</math><br />
<br />
<math>{-K_{s}}=F/s</math><br />
<br />
<math>{-K_{s}}=300N/-.2m</math><br />
<br />
<math>{K_{s}}=1500N/m</math><br />
<br />
===Middling===<br />
Problem: What is the oscillation period of a spiring with spring constant 15N/m with a 30 kg mass attached?<br />
<br />
Solution: <math>T=2π/ω</math> or <math>T=2π√(m/{K_{s}})</math><br />
<br />
<math>{K_{s}}=15N/m)</math> and <math>m=30kg</math><br />
<br />
<math>T=2π√(30kg/15N/m)</math><br />
<br />
<math>T=8.88 seconds</math><br />
<br />
===Difficult===<br />
Problem: A spring with spring constant 18 N/m has mass of 2 kg is attached to it. The mass is then displaced to x = 2 . How much time does it take for the block to travel to the point x = 1?<br />
<br />
Solution:<br />
<br />
<math>x=Acos(ωt)</math><br />
<br />
<math>x/A=cos(√({K_{s}}/m)t)</math><br />
<br />
<math>1/2=cos(√(18N/m/2kg)t)</math><br />
<br />
<math>cos^{-1}(1/2)=3t</math><br />
<br />
<math>t=.35seconds</math><br />
<br />
==Connectedness==<br />
<br />
One interesting application of simple harmonic motion is its ability to approximate the interatomic vibration of molecules which I find very interesting as an Earth and Atmospheric Science major, trying to better understand our environment and how the molecules it is made up of interact. I have always been very intrigued by the composition and interactions of molecules and this approximations brings me another step closer to understanding how our world works. An interesting industrial application of simple harmonic motion is its approximation of a car running on worn down shock absorbers.<br />
<br />
==History==<br />
<br />
Thomas Hooke, an English scientist, created Hooke's Law in 1660 while working on his invention the watch-spring. In the 1660s Hooke gained the title of curator of the Royal Society where he led top experiments for the society. The watch-spring Hooke was working on was one of the first capable of determining longitude at sea by using a spring in simple harmonic motion which has a tendency resist disturbances such as the shakes that could occur while at sea.<br />
<br />
== See also ==<br />
<br />
[[Hooke's Law]]<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
[https://en.wikipedia.org/wiki/Simple_harmonic_motion]<br />
<br />
[[Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=14161Simple Harmonic Motion2015-12-05T14:51:19Z<p>Mmcdaniel: /* Simple */</p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=Acos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2π/ω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
Problem: A spring has a restoring force of 300 N when it is stretched -.2m. What is the spring's constant <math>{K_{s}}</math>. in N/m? <br />
<br />
Solution:<br />
<math>F={-K_{s}}*s}</math><br />
<br />
<math>{-K_{s}}=F/s</math><br />
<br />
<math>{-K_{s}}=300N/-.2m</math><br />
<br />
<math>{K_{s}}=1500N/m</math><br />
<br />
===Middling===<br />
Problem: What is the oscillation period of a spiring with spring constant 15N/m with a 30 kg mass attached?<br />
<br />
Solution: <math>T=2π/ω</math> or <math>T=2π√(m/{K_{s}})</math><br />
<br />
<math>{K_{s}}=15N/m)</math> and <math>m=30kg</math><br />
<br />
<math>T=2π√(30kg/15N/m)</math><br />
<br />
<math>T=8.88 seconds</math><br />
<br />
===Difficult===<br />
Problem: A spring with spring constant 18 N/m has mass of 2 kg is attached to it. The mass is then displaced to x = 2 . How much time does it take for the block to travel to the point x = 1?<br />
<br />
Solution:<br />
<br />
<math>x=Acos(ωt)</math><br />
<br />
<math>x/A=cos(√({K_{s}}/m)t)</math><br />
<br />
<math>1/2=cos(√(18N/m/2kg)t)</math><br />
<br />
<math>cos^{-1}(1/2)=3t</math><br />
<br />
<math>t=.35seconds</math><br />
<br />
==Connectedness==<br />
<br />
One interesting application of simple harmonic motion is its ability to approximate the interatomic vibration of molecules which I find very interesting as an Earth and Atmospheric Science major, trying to better understand our environment and how the molecules it is made up of interact. I have always been very intrigued by the composition and interactions of molecules and this approximations brings me another step closer to understanding how our world works. An interesting industrial application of simple harmonic motion is its approximation of a car running on worn down shock absorbers.<br />
<br />
==History==<br />
<br />
Thomas Hooke, an English scientist, created Hooke's Law in 1660 while working on his invention the watch-spring. In the 1660s Hooke gained the title of curator of the Royal Society where he led top experiments for the society. The watch-spring Hooke was working on was one of the first capable of determining longitude at sea by using a spring in simple harmonic motion which has a tendency resist disturbances such as the shakes that could occur while at sea.<br />
<br />
== See also ==<br />
<br />
[[Hooke's Law]]<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
[https://en.wikipedia.org/wiki/Simple_harmonic_motion]<br />
<br />
[[Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=14160Simple Harmonic Motion2015-12-05T14:50:57Z<p>Mmcdaniel: /* Examples */</p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=Acos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2π/ω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
Problem: A spring has a restoring force of 300 N when it is stretched -.2m. What is the spring's constant <math>{K_{s}}</math>. in N/m? <br />
<br />
Solution:<math>{F}={-K_{s}}*s}</math><br />
<br />
<math>{-K_{s}}=F/s</math><br />
<br />
<math>{-K_{s}}=300N/-.2m</math><br />
<br />
<math>{K_{s}}=1500N/m</math><br />
<br />
===Middling===<br />
Problem: What is the oscillation period of a spiring with spring constant 15N/m with a 30 kg mass attached?<br />
<br />
Solution: <math>T=2π/ω</math> or <math>T=2π√(m/{K_{s}})</math><br />
<br />
<math>{K_{s}}=15N/m)</math> and <math>m=30kg</math><br />
<br />
<math>T=2π√(30kg/15N/m)</math><br />
<br />
<math>T=8.88 seconds</math><br />
<br />
===Difficult===<br />
Problem: A spring with spring constant 18 N/m has mass of 2 kg is attached to it. The mass is then displaced to x = 2 . How much time does it take for the block to travel to the point x = 1?<br />
<br />
Solution:<br />
<br />
<math>x=Acos(ωt)</math><br />
<br />
<math>x/A=cos(√({K_{s}}/m)t)</math><br />
<br />
<math>1/2=cos(√(18N/m/2kg)t)</math><br />
<br />
<math>cos^{-1}(1/2)=3t</math><br />
<br />
<math>t=.35seconds</math><br />
<br />
==Connectedness==<br />
<br />
One interesting application of simple harmonic motion is its ability to approximate the interatomic vibration of molecules which I find very interesting as an Earth and Atmospheric Science major, trying to better understand our environment and how the molecules it is made up of interact. I have always been very intrigued by the composition and interactions of molecules and this approximations brings me another step closer to understanding how our world works. An interesting industrial application of simple harmonic motion is its approximation of a car running on worn down shock absorbers.<br />
<br />
==History==<br />
<br />
Thomas Hooke, an English scientist, created Hooke's Law in 1660 while working on his invention the watch-spring. In the 1660s Hooke gained the title of curator of the Royal Society where he led top experiments for the society. The watch-spring Hooke was working on was one of the first capable of determining longitude at sea by using a spring in simple harmonic motion which has a tendency resist disturbances such as the shakes that could occur while at sea.<br />
<br />
== See also ==<br />
<br />
[[Hooke's Law]]<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
[https://en.wikipedia.org/wiki/Simple_harmonic_motion]<br />
<br />
[[Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=14159Simple Harmonic Motion2015-12-05T14:50:37Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=Acos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2π/ω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
Problem: A spring has a restoring force of 300 N when it is stretched -.2m. What is the spring's constant <math>{K_{s}}</math>. in N/m? <br />
<br />
Solution: <math>{F}={-K_{s}}*s}</math><br />
<br />
<math>{-K_{s}}=F/s</math><br />
<br />
<math>{-K_{s}}=300N/-.2m</math><br />
<br />
<math>{K_{s}}=1500N/m</math><br />
<br />
===Middling===<br />
Problem: What is the oscillation period of a spiring with spring constant 15N/m with a 30 kg mass attached?<br />
<br />
Solution: <math>T=2π/ω</math> or <math>T=2π√(m/{K_{s}})</math><br />
<br />
<math>{K_{s}}=15N/m)</math> and <math>m=30kg</math><br />
<br />
<math>T=2π√(30kg/15N/m)</math><br />
<br />
<math>T=8.88 seconds</math><br />
<br />
===Difficult===<br />
Problem: A spring with spring constant 18 N/m has mass of 2 kg is attached to it. The mass is then displaced to x = 2 . How much time does it take for the block to travel to the point x = 1?<br />
<br />
Solution:<br />
<br />
<math>x=Acos(ωt)</math><br />
<br />
<math>x/A=cos(√({K_{s}}/m)t)</math><br />
<br />
<math>1/2=cos(√(18N/m/2kg)t)</math><br />
<br />
<math>cos^{-1}(1/2)=3t</math><br />
<br />
<math>t=.35seconds</math><br />
<br />
==Connectedness==<br />
<br />
One interesting application of simple harmonic motion is its ability to approximate the interatomic vibration of molecules which I find very interesting as an Earth and Atmospheric Science major, trying to better understand our environment and how the molecules it is made up of interact. I have always been very intrigued by the composition and interactions of molecules and this approximations brings me another step closer to understanding how our world works. An interesting industrial application of simple harmonic motion is its approximation of a car running on worn down shock absorbers.<br />
<br />
==History==<br />
<br />
Thomas Hooke, an English scientist, created Hooke's Law in 1660 while working on his invention the watch-spring. In the 1660s Hooke gained the title of curator of the Royal Society where he led top experiments for the society. The watch-spring Hooke was working on was one of the first capable of determining longitude at sea by using a spring in simple harmonic motion which has a tendency resist disturbances such as the shakes that could occur while at sea.<br />
<br />
== See also ==<br />
<br />
[[Hooke's Law]]<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
[https://en.wikipedia.org/wiki/Simple_harmonic_motion]<br />
<br />
[[Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=14155Simple Harmonic Motion2015-12-05T14:38:46Z<p>Mmcdaniel: /* Examples */</p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=Acos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2π/ω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
<br />
===Middling===<br />
Problem: What is the oscillation period of a spiring with spring constant 15N/m with a 30 kg mass attached?<br />
<br />
Solution: <math>T=2π/ω</math> or <math>T=2π√(m/{K_{s}})</math><br />
<br />
<math>{K_{s}}=15N/m)</math> and <math>m=30kg</math><br />
<br />
<math>T=2π√(30kg/15N/m)</math><br />
<br />
<math>T=8.88 seconds</math><br />
<br />
===Difficult===<br />
Problem: A spring with spring constant 18 N/m has mass of 2 kg is attached to it. The mass is then displaced to x = 2 . How much time does it take for the block to travel to the point x = 1?<br />
<br />
Solution:<br />
<br />
<math>x=Acos(ωt)</math><br />
<br />
<math>x/A=cos(√({K_{s}}/m)t)</math><br />
<br />
<math>1/2=cos(√(18N/m/2kg)t)</math><br />
<br />
<math>cos^{-1}(1/2)=3t</math><br />
<br />
<math>t=.35seconds</math><br />
<br />
==Connectedness==<br />
<br />
One interesting application of simple harmonic motion is its ability to approximate the interatomic vibration of molecules which I find very interesting as an Earth and Atmospheric Science major, trying to better understand our environment and how the molecules it is made up of interact. I have always been very intrigued by the composition and interactions of molecules and this approximations brings me another step closer to understanding how our world works. An interesting industrial application of simple harmonic motion is its approximation of a car running on worn down shock absorbers.<br />
<br />
==History==<br />
<br />
Thomas Hooke, an English scientist, created Hooke's Law in 1660 while working on his invention the watch-spring. In the 1660s Hooke gained the title of curator of the Royal Society where he led top experiments for the society. The watch-spring Hooke was working on was one of the first capable of determining longitude at sea by using a spring in simple harmonic motion which has a tendency resist disturbances such as the shakes that could occur while at sea.<br />
<br />
== See also ==<br />
<br />
[[Hooke's Law]]<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
[https://en.wikipedia.org/wiki/Simple_harmonic_motion]<br />
<br />
[[Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=14154Simple Harmonic Motion2015-12-05T14:37:52Z<p>Mmcdaniel: /* Examples */</p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=Acos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2π/ω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
<br />
===Middling===<br />
Problem: What is the oscillation period of a spiring with spring constant 15N/m with a 30 kg mass attached?<br />
<br />
Solution: <math>T=2π/ω</math> or <math>T=2π√(m/{K_{s}})</math><br />
<br />
<math>{K_{s}}=15N/m)</math> and <math>m=30kg</math><br />
<br />
<math>T=2π√(30kg/15N/m)</math><br />
<br />
<math>T=8.88 seconds</math><br />
<br />
===Difficult===<br />
Problem: A spring with spring constant 18 N/m has mass of 2 kg is attached to it. The mass is then displaced to x = 2 . How much time does it take for the block to travel to the point x = 1?<br />
<br />
Solution:<br />
<br />
<math>x=Acos(ωt)</math><br />
<br />
<math>x/A=cos(√({K_{s}}/m)t)</math><br />
<br />
<math>1/2=cos(√(18N/m/2kg)t)</math><br />
<br />
<math>cos^{-1}(1/2)=3t</math><br />
<br />
==Connectedness==<br />
<br />
One interesting application of simple harmonic motion is its ability to approximate the interatomic vibration of molecules which I find very interesting as an Earth and Atmospheric Science major, trying to better understand our environment and how the molecules it is made up of interact. I have always been very intrigued by the composition and interactions of molecules and this approximations brings me another step closer to understanding how our world works. An interesting industrial application of simple harmonic motion is its approximation of a car running on worn down shock absorbers.<br />
<br />
==History==<br />
<br />
Thomas Hooke, an English scientist, created Hooke's Law in 1660 while working on his invention the watch-spring. In the 1660s Hooke gained the title of curator of the Royal Society where he led top experiments for the society. The watch-spring Hooke was working on was one of the first capable of determining longitude at sea by using a spring in simple harmonic motion which has a tendency resist disturbances such as the shakes that could occur while at sea.<br />
<br />
== See also ==<br />
<br />
[[Hooke's Law]]<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
[https://en.wikipedia.org/wiki/Simple_harmonic_motion]<br />
<br />
[[Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=14153Simple Harmonic Motion2015-12-05T14:37:16Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=Acos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2π/ω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
<br />
===Middling===<br />
Problem: What is the oscillation period of a spiring with spring constant 15N/m with a 30 kg mass attached?<br />
<br />
Solution: <math>T=2π/ω</math> or <math>T=2π√(m/{K_{s}})</math><br />
<br />
<math>{K_{s}}=15N/m)</math> and <math>m=30kg</math><br />
<br />
<math>T=2π√(30kg/15N/m)</math><br />
<br />
<math>T=8.88 seconds</math><br />
<br />
===Difficult===<br />
Problem: A spring with spring constant 18 N/m has mass of 2 kg is attached to it. The mass is then displaced to x = 2 . How much time does it take for the block to travel to the point x = 1?<br />
<br />
Solution:<br />
<br />
<math>x=Acos(ωt)</math><br />
<br />
<math>x/A=cos(√({K_{s}}/m)t)</math><br />
<br />
<math>1/2=cos(√(18N/m/2kg)t)</math><br />
<br />
<math>cos^(-1)(1/2)=3t</math><br />
<br />
==Connectedness==<br />
<br />
One interesting application of simple harmonic motion is its ability to approximate the interatomic vibration of molecules which I find very interesting as an Earth and Atmospheric Science major, trying to better understand our environment and how the molecules it is made up of interact. I have always been very intrigued by the composition and interactions of molecules and this approximations brings me another step closer to understanding how our world works. An interesting industrial application of simple harmonic motion is its approximation of a car running on worn down shock absorbers.<br />
<br />
==History==<br />
<br />
Thomas Hooke, an English scientist, created Hooke's Law in 1660 while working on his invention the watch-spring. In the 1660s Hooke gained the title of curator of the Royal Society where he led top experiments for the society. The watch-spring Hooke was working on was one of the first capable of determining longitude at sea by using a spring in simple harmonic motion which has a tendency resist disturbances such as the shakes that could occur while at sea.<br />
<br />
== See also ==<br />
<br />
[[Hooke's Law]]<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
[https://en.wikipedia.org/wiki/Simple_harmonic_motion]<br />
<br />
[[Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=14152Simple Harmonic Motion2015-12-05T14:36:54Z<p>Mmcdaniel: /* Difficult */</p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=Acos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2π/ω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
<br />
===Middling===<br />
Problem: What is the oscillation period of a spiring with spring constant 15N/m with a 30 kg mass attached?<br />
<br />
Solution: <math>T=2π/ω</math> or <math>T=2π√(m/{K_{s}})</math><br />
<br />
<math>{K_{s}}=15N/m)</math> and <math>m=30kg</math><br />
<br />
<math>T=2π√(30kg/15N/m)</math><br />
<br />
<math>T=8.88 seconds</math><br />
<br />
===Difficult===<br />
Problem: A spring with spring constant 18 N/m has mass of 2 kg is attached to it. The mass is then displaced to x = 2 . How much time does it take for the block to travel to the point x = 1?<br />
<br />
Solution:<br />
<br />
<math>x=Acos(ωt)</math><br />
<br />
<math>x/A=cos(√({K_{s}}/m)t)</math><br />
<br />
<math>1/2=cos(√(18N/m/2kg)t)</math><br />
<br />
<math>cos^-(1)(1/2)=3t</math><br />
<br />
==Connectedness==<br />
<br />
One interesting application of simple harmonic motion is its ability to approximate the interatomic vibration of molecules which I find very interesting as an Earth and Atmospheric Science major, trying to better understand our environment and how the molecules it is made up of interact. I have always been very intrigued by the composition and interactions of molecules and this approximations brings me another step closer to understanding how our world works. An interesting industrial application of simple harmonic motion is its approximation of a car running on worn down shock absorbers.<br />
<br />
==History==<br />
<br />
Thomas Hooke, an English scientist, created Hooke's Law in 1660 while working on his invention the watch-spring. In the 1660s Hooke gained the title of curator of the Royal Society where he led top experiments for the society. The watch-spring Hooke was working on was one of the first capable of determining longitude at sea by using a spring in simple harmonic motion which has a tendency resist disturbances such as the shakes that could occur while at sea.<br />
<br />
== See also ==<br />
<br />
[[Hooke's Law]]<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
[https://en.wikipedia.org/wiki/Simple_harmonic_motion]<br />
<br />
[[Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=14151Simple Harmonic Motion2015-12-05T14:36:30Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=Acos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2π/ω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
<br />
===Middling===<br />
Problem: What is the oscillation period of a spiring with spring constant 15N/m with a 30 kg mass attached?<br />
<br />
Solution: <math>T=2π/ω</math> or <math>T=2π√(m/{K_{s}})</math><br />
<br />
<math>{K_{s}}=15N/m)</math> and <math>m=30kg</math><br />
<br />
<math>T=2π√(30kg/15N/m)</math><br />
<br />
<math>T=8.88 seconds</math><br />
<br />
===Difficult===<br />
Problem: A spring with spring constant 18 N/m has mass of 2 kg is attached to it. The mass is then displaced to x = 2 . How much time does it take for the block to travel to the point x = 1?<br />
<br />
Solution:<br />
<br />
<math>x=Acos(ωt)</math><br />
<br />
<math>x/A=cos(√({K_{s}}/m)t)</math><br />
<br />
<math>1/2=cos(√(18N/m/2kg)t)</math><br />
<br />
<math>cos^-{1}(1/2)=3t</math><br />
<br />
==Connectedness==<br />
<br />
One interesting application of simple harmonic motion is its ability to approximate the interatomic vibration of molecules which I find very interesting as an Earth and Atmospheric Science major, trying to better understand our environment and how the molecules it is made up of interact. I have always been very intrigued by the composition and interactions of molecules and this approximations brings me another step closer to understanding how our world works. An interesting industrial application of simple harmonic motion is its approximation of a car running on worn down shock absorbers.<br />
<br />
==History==<br />
<br />
Thomas Hooke, an English scientist, created Hooke's Law in 1660 while working on his invention the watch-spring. In the 1660s Hooke gained the title of curator of the Royal Society where he led top experiments for the society. The watch-spring Hooke was working on was one of the first capable of determining longitude at sea by using a spring in simple harmonic motion which has a tendency resist disturbances such as the shakes that could occur while at sea.<br />
<br />
== See also ==<br />
<br />
[[Hooke's Law]]<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
[https://en.wikipedia.org/wiki/Simple_harmonic_motion]<br />
<br />
[[Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=14150Simple Harmonic Motion2015-12-05T14:35:52Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=Acos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2π/ω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
<br />
===Middling===<br />
Problem: What is the oscillation period of a spiring with spring constant 15N/m with a 30 kg mass attached?<br />
<br />
Solution: <math>T=2π/ω</math> or <math>T=2π√(m/{K_{s}})</math><br />
<br />
<math>{K_{s}}=15N/m)</math> and <math>m=30kg</math><br />
<br />
<math>T=2π√(30kg/15N/m)</math><br />
<br />
<math>T=8.88 seconds</math><br />
<br />
===Difficult===<br />
Problem: A spring with spring constant 18 N/m has mass of 2 kg is attached to it. The mass is then displaced to x = 2 . How much time does it take for the block to travel to the point x = 1?<br />
<br />
Solution:<br />
<br />
<math>x=Acos(ωt)</math><br />
<br />
<math>x/A=cos(√({K_{s}}/m)t)</math><br />
<br />
<math>1/2=cos(√(18N/m/2kg)t)</math><br />
<br />
<math>cos^-1(1/2)=3t</math><br />
<br />
==Connectedness==<br />
<br />
One interesting application of simple harmonic motion is its ability to approximate the interatomic vibration of molecules which I find very interesting as an Earth and Atmospheric Science major, trying to better understand our environment and how the molecules it is made up of interact. I have always been very intrigued by the composition and interactions of molecules and this approximations brings me another step closer to understanding how our world works. An interesting industrial application of simple harmonic motion is its approximation of a car running on worn down shock absorbers.<br />
<br />
==History==<br />
<br />
Thomas Hooke, an English scientist, created Hooke's Law in 1660 while working on his invention the watch-spring. In the 1660s Hooke gained the title of curator of the Royal Society where he led top experiments for the society. The watch-spring Hooke was working on was one of the first capable of determining longitude at sea by using a spring in simple harmonic motion which has a tendency resist disturbances such as the shakes that could occur while at sea.<br />
<br />
== See also ==<br />
<br />
[[Hooke's Law]]<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
[https://en.wikipedia.org/wiki/Simple_harmonic_motion]<br />
<br />
[[Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=14146Simple Harmonic Motion2015-12-05T14:33:18Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=Acos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2π/ω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
<br />
===Middling===<br />
Problem: What is the oscillation period of a spiring with spring constant 15N/m with a 30 kg mass attached?<br />
<br />
Solution: <math>T=2π/ω</math> or <math>T=2π√(m/{K_{s}})</math><br />
<br />
<math>{K_{s}}=15N/m)</math> and <math>m=30kg</math><br />
<br />
<math>T=2π√(30kg/15N/m)</math><br />
<br />
<math>T=8.88 seconds</math><br />
<br />
===Difficult===<br />
Problem: A spring with spring constant 18 N/m has mass of 2 kg is attached to it. The mass is then displaced to x = 2 . How much time does it take for the block to travel to the point x = 1?<br />
<br />
Solution:<br />
<br />
<math>x=Acos(ωt)</math><br />
<br />
<math>x/A=cos(√({K_{s}}/m)t)</math><br />
<br />
<math>1/2=cos(√(18N/m/2kg)t)</math><br />
<br />
==Connectedness==<br />
<br />
One interesting application of simple harmonic motion is its ability to approximate the interatomic vibration of molecules which I find very interesting as an Earth and Atmospheric Science major, trying to better understand our environment and how the molecules it is made up of interact. I have always been very intrigued by the composition and interactions of molecules and this approximations brings me another step closer to understanding how our world works. An interesting industrial application of simple harmonic motion is its approximation of a car running on worn down shock absorbers.<br />
<br />
==History==<br />
<br />
Thomas Hooke, an English scientist, created Hooke's Law in 1660 while working on his invention the watch-spring. In the 1660s Hooke gained the title of curator of the Royal Society where he led top experiments for the society. The watch-spring Hooke was working on was one of the first capable of determining longitude at sea by using a spring in simple harmonic motion which has a tendency resist disturbances such as the shakes that could occur while at sea.<br />
<br />
== See also ==<br />
<br />
[[Hooke's Law]]<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
[https://en.wikipedia.org/wiki/Simple_harmonic_motion]<br />
<br />
[[Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=14141Simple Harmonic Motion2015-12-05T14:26:49Z<p>Mmcdaniel: /* Difficult */</p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=cos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2π/ω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
<br />
===Middling===<br />
Problem: What is the oscillation period of a spiring with spring constant 15N/m with a 30 kg mass attached?<br />
<br />
Solution: <math>T=2π/ω</math> or <math>T=2π√(m/{K_{s}})</math><br />
<br />
<math>{K_{s}}=15N/m)</math> and <math>m=30kg</math><br />
<br />
<math>T=2π√(30kg/15N/m)</math><br />
<br />
<math>T=8.88 seconds</math><br />
<br />
===Difficult===<br />
Problem: A spring with spring constant 18 N/m has mass of 2 kg is attached to it. The mass is then displaced to x = 2 . How much time does it take for the block to travel to the point x = 1?<br />
<br />
Solution:<br />
<br />
==Connectedness==<br />
<br />
One interesting application of simple harmonic motion is its ability to approximate the interatomic vibration of molecules which I find very interesting as an Earth and Atmospheric Science major, trying to better understand our environment and how the molecules it is made up of interact. I have always been very intrigued by the composition and interactions of molecules and this approximations brings me another step closer to understanding how our world works. An interesting industrial application of simple harmonic motion is its approximation of a car running on worn down shock absorbers.<br />
<br />
==History==<br />
<br />
Thomas Hooke, an English scientist, created Hooke's Law in 1660 while working on his invention the watch-spring. In the 1660s Hooke gained the title of curator of the Royal Society where he led top experiments for the society. The watch-spring Hooke was working on was one of the first capable of determining longitude at sea by using a spring in simple harmonic motion which has a tendency resist disturbances such as the shakes that could occur while at sea.<br />
<br />
== See also ==<br />
<br />
[[Hooke's Law]]<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
[https://en.wikipedia.org/wiki/Simple_harmonic_motion]<br />
<br />
[[Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=14138Simple Harmonic Motion2015-12-05T14:24:21Z<p>Mmcdaniel: /* Middling */</p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=cos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2π/ω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
<br />
===Middling===<br />
Problem: What is the oscillation period of a spiring with spring constant 15N/m with a 30 kg mass attached?<br />
<br />
Solution: <math>T=2π/ω</math> or <math>T=2π√(m/{K_{s}})</math><br />
<br />
<math>{K_{s}}=15N/m)</math> and <math>m=30kg</math><br />
<br />
<math>T=2π√(30kg/15N/m)</math><br />
<br />
<math>T=8.88 seconds</math><br />
<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
One interesting application of simple harmonic motion is its ability to approximate the interatomic vibration of molecules which I find very interesting as an Earth and Atmospheric Science major, trying to better understand our environment and how the molecules it is made up of interact. I have always been very intrigued by the composition and interactions of molecules and this approximations brings me another step closer to understanding how our world works. An interesting industrial application of simple harmonic motion is its approximation of a car running on worn down shock absorbers.<br />
<br />
==History==<br />
<br />
Thomas Hooke, an English scientist, created Hooke's Law in 1660 while working on his invention the watch-spring. In the 1660s Hooke gained the title of curator of the Royal Society where he led top experiments for the society. The watch-spring Hooke was working on was one of the first capable of determining longitude at sea by using a spring in simple harmonic motion which has a tendency resist disturbances such as the shakes that could occur while at sea.<br />
<br />
== See also ==<br />
<br />
[[Hooke's Law]]<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
[https://en.wikipedia.org/wiki/Simple_harmonic_motion]<br />
<br />
[[Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=14135Simple Harmonic Motion2015-12-05T14:19:56Z<p>Mmcdaniel: /* Middling */</p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=cos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2π/ω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
<br />
===Middling===<br />
Problem: What is the oscillation period of a spiring with spring constant 15N/m with a 30 kg mass attached?<br />
<br />
Solution: <math>T=2π/ω</math> or <math>T=2π√(m/{K_{s}})</math><br />
<math>{K_{s}}=15N/m)</math> and <math>m=30kg</math><br />
<math>T=2π√(30kg/15N/m)</math><br />
<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
One interesting application of simple harmonic motion is its ability to approximate the interatomic vibration of molecules which I find very interesting as an Earth and Atmospheric Science major, trying to better understand our environment and how the molecules it is made up of interact. I have always been very intrigued by the composition and interactions of molecules and this approximations brings me another step closer to understanding how our world works. An interesting industrial application of simple harmonic motion is its approximation of a car running on worn down shock absorbers.<br />
<br />
==History==<br />
<br />
Thomas Hooke, an English scientist, created Hooke's Law in 1660 while working on his invention the watch-spring. In the 1660s Hooke gained the title of curator of the Royal Society where he led top experiments for the society. The watch-spring Hooke was working on was one of the first capable of determining longitude at sea by using a spring in simple harmonic motion which has a tendency resist disturbances such as the shakes that could occur while at sea.<br />
<br />
== See also ==<br />
<br />
[[Hooke's Law]]<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
[https://en.wikipedia.org/wiki/Simple_harmonic_motion]<br />
<br />
[[Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=14134Simple Harmonic Motion2015-12-05T14:19:36Z<p>Mmcdaniel: /* Middling */</p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=cos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2π/ω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
<br />
===Middling===<br />
Problem: What is the oscillation period of a spiring with spring constant 15N/m with a 30 kg mass attached?<br />
Solution: <br />
<math>T=2π/ω</math> or <math>T=2π√(m/{K_{s}})</math><br />
<math>{K_{s}}=15N/m)</math> and <math>m=30kg</math><br />
<math>T=2π√(30kg/15N/m)</math><br />
<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
One interesting application of simple harmonic motion is its ability to approximate the interatomic vibration of molecules which I find very interesting as an Earth and Atmospheric Science major, trying to better understand our environment and how the molecules it is made up of interact. I have always been very intrigued by the composition and interactions of molecules and this approximations brings me another step closer to understanding how our world works. An interesting industrial application of simple harmonic motion is its approximation of a car running on worn down shock absorbers.<br />
<br />
==History==<br />
<br />
Thomas Hooke, an English scientist, created Hooke's Law in 1660 while working on his invention the watch-spring. In the 1660s Hooke gained the title of curator of the Royal Society where he led top experiments for the society. The watch-spring Hooke was working on was one of the first capable of determining longitude at sea by using a spring in simple harmonic motion which has a tendency resist disturbances such as the shakes that could occur while at sea.<br />
<br />
== See also ==<br />
<br />
[[Hooke's Law]]<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
[https://en.wikipedia.org/wiki/Simple_harmonic_motion]<br />
<br />
[[Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=14133Simple Harmonic Motion2015-12-05T14:19:10Z<p>Mmcdaniel: /* Middling */</p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=cos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2π/ω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
<br />
===Middling===<br />
Problem: What is the oscillation period of a spiring with spring constant 15N/m with a 30 kg mass attached?<br />
Solution: <br />
<math>T=2π/ω</math> or <math>T=2π√(m/{K_{s}})</math><br />
<math>{K_{s}}=15N/m)</math> and <math>m=30kg</math><br />
<math>T=2π√(30kg/15N/m)</math><br />
<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
One interesting application of simple harmonic motion is its ability to approximate the interatomic vibration of molecules which I find very interesting as an Earth and Atmospheric Science major, trying to better understand our environment and how the molecules it is made up of interact. I have always been very intrigued by the composition and interactions of molecules and this approximations brings me another step closer to understanding how our world works. An interesting industrial application of simple harmonic motion is its approximation of a car running on worn down shock absorbers.<br />
<br />
==History==<br />
<br />
Thomas Hooke, an English scientist, created Hooke's Law in 1660 while working on his invention the watch-spring. In the 1660s Hooke gained the title of curator of the Royal Society where he led top experiments for the society. The watch-spring Hooke was working on was one of the first capable of determining longitude at sea by using a spring in simple harmonic motion which has a tendency resist disturbances such as the shakes that could occur while at sea.<br />
<br />
== See also ==<br />
<br />
[[Hooke's Law]]<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
[https://en.wikipedia.org/wiki/Simple_harmonic_motion]<br />
<br />
[[Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=14132Simple Harmonic Motion2015-12-05T14:18:28Z<p>Mmcdaniel: /* Middling */</p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=cos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2π/ω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
<br />
===Middling===<br />
Problem: What is the oscillation period of a spiring with spring constant 15N/m with a 30 kg mass attached?<br />
Solution: <math>T=2π/ω</math> or <math>T=2π√(m/{K_{s}})</math><br />
<math>{K_{s}}=15N/m)</math> and <math>m=30kg</math><br />
<math>T=2π√(30kg/15N/m)</math><br />
<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
One interesting application of simple harmonic motion is its ability to approximate the interatomic vibration of molecules which I find very interesting as an Earth and Atmospheric Science major, trying to better understand our environment and how the molecules it is made up of interact. I have always been very intrigued by the composition and interactions of molecules and this approximations brings me another step closer to understanding how our world works. An interesting industrial application of simple harmonic motion is its approximation of a car running on worn down shock absorbers.<br />
<br />
==History==<br />
<br />
Thomas Hooke, an English scientist, created Hooke's Law in 1660 while working on his invention the watch-spring. In the 1660s Hooke gained the title of curator of the Royal Society where he led top experiments for the society. The watch-spring Hooke was working on was one of the first capable of determining longitude at sea by using a spring in simple harmonic motion which has a tendency resist disturbances such as the shakes that could occur while at sea.<br />
<br />
== See also ==<br />
<br />
[[Hooke's Law]]<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
[https://en.wikipedia.org/wiki/Simple_harmonic_motion]<br />
<br />
[[Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=14130Simple Harmonic Motion2015-12-05T14:18:00Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=cos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2π/ω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
<br />
===Middling===<br />
Problem: What is the oscillation period of a spiring with spring constant 15N/m with a 30 kg mass attached?<br />
Solution: <math>T=2π/ω</math> or <math>T=2π√(m/{K_{s}})</math>.<br />
<math>{K_{s}}=15N/m)</math> and <math>m=30kg</math><br />
<math>T=2π√(30kg/15N/m)</math><br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
One interesting application of simple harmonic motion is its ability to approximate the interatomic vibration of molecules which I find very interesting as an Earth and Atmospheric Science major, trying to better understand our environment and how the molecules it is made up of interact. I have always been very intrigued by the composition and interactions of molecules and this approximations brings me another step closer to understanding how our world works. An interesting industrial application of simple harmonic motion is its approximation of a car running on worn down shock absorbers.<br />
<br />
==History==<br />
<br />
Thomas Hooke, an English scientist, created Hooke's Law in 1660 while working on his invention the watch-spring. In the 1660s Hooke gained the title of curator of the Royal Society where he led top experiments for the society. The watch-spring Hooke was working on was one of the first capable of determining longitude at sea by using a spring in simple harmonic motion which has a tendency resist disturbances such as the shakes that could occur while at sea.<br />
<br />
== See also ==<br />
<br />
[[Hooke's Law]]<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
[https://en.wikipedia.org/wiki/Simple_harmonic_motion]<br />
<br />
[[Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=14128Simple Harmonic Motion2015-12-05T14:16:02Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=cos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2π/ω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
<br />
===Middling===<br />
Problem: What is the oscillation period of a spiring with spring constant 15N/m with a 30 kg mass attached?<br />
Solution: <math>T=2π/ω</math>. or T=<math>T=2π√(m/{K_{s}})</math>.<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
One interesting application of simple harmonic motion is its ability to approximate the interatomic vibration of molecules which I find very interesting as an Earth and Atmospheric Science major, trying to better understand our environment and how the molecules it is made up of interact. I have always been very intrigued by the composition and interactions of molecules and this approximations brings me another step closer to understanding how our world works. An interesting industrial application of simple harmonic motion is its approximation of a car running on worn down shock absorbers.<br />
<br />
==History==<br />
<br />
Thomas Hooke, an English scientist, created Hooke's Law in 1660 while working on his invention the watch-spring. In the 1660s Hooke gained the title of curator of the Royal Society where he led top experiments for the society. The watch-spring Hooke was working on was one of the first capable of determining longitude at sea by using a spring in simple harmonic motion which has a tendency resist disturbances such as the shakes that could occur while at sea.<br />
<br />
== See also ==<br />
<br />
[[Hooke's Law]]<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
[https://en.wikipedia.org/wiki/Simple_harmonic_motion]<br />
<br />
[[Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=14116Simple Harmonic Motion2015-12-05T14:08:51Z<p>Mmcdaniel: /* A Mathematical Model */</p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=cos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2π/ω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
One interesting application of simple harmonic motion is its ability to approximate the interatomic vibration of molecules which I find very interesting as an Earth and Atmospheric Science major, trying to better understand our environment and how the molecules it is made up of interact. I have always been very intrigued by the composition and interactions of molecules and this approximations brings me another step closer to understanding how our world works. An interesting industrial application of simple harmonic motion is its approximation of a car running on worn down shock absorbers.<br />
<br />
==History==<br />
<br />
Thomas Hooke, an English scientist, created Hooke's Law in 1660 while working on his invention the watch-spring. In the 1660s Hooke gained the title of curator of the Royal Society where he led top experiments for the society. The watch-spring Hooke was working on was one of the first capable of determining longitude at sea by using a spring in simple harmonic motion which has a tendency resist disturbances such as the shakes that could occur while at sea.<br />
<br />
== See also ==<br />
<br />
[[Hooke's Law]]<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
[https://en.wikipedia.org/wiki/Simple_harmonic_motion]<br />
<br />
[[Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=13042Simple Harmonic Motion2015-12-05T01:36:20Z<p>Mmcdaniel: /* History */</p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=cos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2πω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
One interesting application of simple harmonic motion is its ability to approximate the interatomic vibration of molecules which I find very interesting as an Earth and Atmospheric Science major, trying to better understand our environment and how the molecules it is made up of interact. I have always been very intrigued by the composition and interactions of molecules and this approximations brings me another step closer to understanding how our world works. An interesting industrial application of simple harmonic motion is its approximation of a car running on worn down shock absorbers.<br />
<br />
==History==<br />
<br />
Thomas Hooke, an English scientist, created Hooke's Law in 1660 while working on his invention the watch-spring. In the 1660s Hooke gained the title of curator of the Royal Society where he led top experiments for the society. The watch-spring Hooke was working on was one of the first capable of determining longitude at sea by using a spring in simple harmonic motion which has a tendency resist disturbances such as the shakes that could occur while at sea.<br />
<br />
== See also ==<br />
<br />
[[Hooke's Law]]<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
[https://en.wikipedia.org/wiki/Simple_harmonic_motion]<br />
<br />
[[Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=13040Simple Harmonic Motion2015-12-05T01:35:56Z<p>Mmcdaniel: /* History */</p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=cos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2πω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
One interesting application of simple harmonic motion is its ability to approximate the interatomic vibration of molecules which I find very interesting as an Earth and Atmospheric Science major, trying to better understand our environment and how the molecules it is made up of interact. I have always been very intrigued by the composition and interactions of molecules and this approximations brings me another step closer to understanding how our world works. An interesting industrial application of simple harmonic motion is its approximation of a car running on worn down shock absorbers.<br />
<br />
==History==<br />
<br />
Thomas Hooke, an English scientist, created Hooke's Law in 1660 while working on his invention the watch-spring. In the 1660s Hooke gained the title of curator of the Royal Society where he led top experiments for the society. The watch-spring Hooke was working on was one of the first capable of determining longitude at sea by using a spring in simple harmonic motion which has a tendency resist disturbances such as the shakes that could occur while at sea.<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
[[Hooke's Law]]<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
[https://en.wikipedia.org/wiki/Simple_harmonic_motion]<br />
<br />
[[Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=13010Simple Harmonic Motion2015-12-05T01:14:50Z<p>Mmcdaniel: /* Connectedness */</p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=cos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2πω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
One interesting application of simple harmonic motion is its ability to approximate the interatomic vibration of molecules which I find very interesting as an Earth and Atmospheric Science major, trying to better understand our environment and how the molecules it is made up of interact. I have always been very intrigued by the composition and interactions of molecules and this approximations brings me another step closer to understanding how our world works. An interesting industrial application of simple harmonic motion is its approximation of a car running on worn down shock absorbers.<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
[[Hooke's Law]]<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
[https://en.wikipedia.org/wiki/Simple_harmonic_motion]<br />
<br />
[[Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=12994Simple Harmonic Motion2015-12-05T00:55:59Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=cos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2πω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
[[Hooke's Law]]<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
[https://en.wikipedia.org/wiki/Simple_harmonic_motion]<br />
<br />
[[Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=12978Simple Harmonic Motion2015-12-05T00:46:13Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=cos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2πω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
[https://en.wikipedia.org/wiki/Simple_harmonic_motion]<br />
<br />
[[Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=12946Simple Harmonic Motion2015-12-05T00:31:44Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=cos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2πω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
[https://en.wikipedia.org/wiki/Simple_harmonic_motion]<br />
<br />
[[Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=12945Simple Harmonic Motion2015-12-05T00:31:31Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=cos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2πω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
[https://en.wikipedia.org/wiki/Simple_harmonic_motion]<br />
<br />
[[Category: Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=12944Simple Harmonic Motion2015-12-05T00:29:58Z<p>Mmcdaniel: /* References */</p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=cos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2πω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
[https://en.wikipedia.org/wiki/Simple_harmonic_motion]<br />
<br />
[[Category:Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=12943Simple Harmonic Motion2015-12-05T00:29:06Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=cos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2πω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
[https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion]<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html]<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
<br />
==References==<br />
[https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Simple_Harmonic_Motion/Mathematical_Derivation]<br />
[http://azimadli.com/vibman/simpleharmonicmotion.htm]<br />
<br />
[[Category:Which Category did you place this in?]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=12941Simple Harmonic Motion2015-12-05T00:24:49Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=cos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2πω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/glowscript/5de153d737?toggleCode=true simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br />
<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=12940Simple Harmonic Motion2015-12-05T00:23:54Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=cos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2πω</math>.<br />
<br />
===A Computational Model===<br />
<br />
Click here to see a spring-mass system displaying [https://trinket.io/library/trinkets/5de153d737 simple harmonic motion in vPthyon]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br />
<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=12906Simple Harmonic Motion2015-12-05T00:09:04Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[Image:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=cos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2πω</math>.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Spring-Mass]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br />
<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=File:SHM.png&diff=12901File:SHM.png2015-12-05T00:07:06Z<p>Mmcdaniel: </p>
<hr />
<div></div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=12899Simple Harmonic Motion2015-12-05T00:06:33Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. [[File:SHM.png]]<br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=cos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2πω</math>.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Spring-Mass]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br />
<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=12895Simple Harmonic Motion2015-12-05T00:03:02Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. <br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=cos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2πω</math>.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Spring-Mass]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br />
<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=12870Simple Harmonic Motion2015-12-04T23:50:54Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. <br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=cos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2πω</math>.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br />
<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=12868Simple Harmonic Motion2015-12-04T23:50:36Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. <br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=cos(ωt)</math> where <math>ω=√({K_{s}}/m)</math>. From this equation we can determine that the period for this function, or the time it takes an object to make one complete cycle of motion, to be <math>T=2πω</math>. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br />
<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=12858Simple Harmonic Motion2015-12-04T23:45:53Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. <br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=cos(ωt)</math> where <math>ω=√({K_{s}}/m)</math> For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br />
<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=12856Simple Harmonic Motion2015-12-04T23:43:43Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. <br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. The solution to this differential equation is <math>x=cos(ωt)</math> where <math>ω=sqrt</math> For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br />
<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=12792Simple Harmonic Motion2015-12-04T22:45:22Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. <br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] and [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's Law] which is a first order linear approximation for forces acting on an elastic system, such as a spring. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br />
<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=12784Simple Harmonic Motion2015-12-04T22:42:51Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. <br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>\vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math>. This equations stems from [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's Second Law] For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br />
<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=12752Simple Harmonic Motion2015-12-04T22:25:22Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. <br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}</math> For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br />
<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=12749Simple Harmonic Motion2015-12-04T22:24:47Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. <br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>vec{F}={-K_{s}}*s*\vec{Lhat}</math> where <math>s=L-{L_{o}}<\math> For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br />
<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=12746Simple Harmonic Motion2015-12-04T22:23:50Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. <br />
<br />
===A Mathematical Model===<br />
<br />
The force of this system can be found using <math>vec{F}={-K_{s}}*s*vec{Lhat}</math> where <math>s=L-{L_{o}} For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br />
<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=12735Simple Harmonic Motion2015-12-04T22:15:26Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. A common example of simple harmonic motion is an undamped spring-mass system, or one that does not proceed to rest due to friction or another dissipative force. <br />
<br />
===A Mathematical Model===<br />
<br />
What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br />
<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=12696Simple Harmonic Motion2015-12-04T22:02:10Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.<br />
<br />
==The Main Idea==<br />
<br />
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats. <br />
<br />
<br />
===A Mathematical Model===<br />
<br />
What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br />
<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=4359Simple Harmonic Motion2015-11-30T13:03:22Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
== Introduction ==<br />
<br />
The two major components in Physics II are interactions between electric fields and magnetic fields. This broad subject focuses from a simple topic, electric fields to a much complex idea, electromagnetic radiation. Though this course is very broad in terms of materials that it covers, each topic is very important in understanding the phenomena of electric and magnetic interactions between particles (protons, electrons, dipoles, point charge, capacitor, and, etc), as omitting one concept out of hundreds of concept could lead one approaching the problem differently. This Wiki Page will discuss Chapter 21 of the Matters and Interactions Text Book, 4th edition (Patterns of Field in Space), specifically Gauss's Law and Electric Flux. In order to understand these concepts, one first need to understand the definition of electric field and know each component of Gauss's Law. <br />
<br />
== Dynamics ==<br />
<br />
"Electric Flux" is a quantitative measure of the amount and direction of electric field over an entire surface of a specified object. There are two components in electric flux: direction of the electric field and magnitude of the electric field. These two sums up and give us the value, electric flux, which has a unit of Vm. In order to determine the direction of the electric field of an object, one need to figure out the x,y,z coordinates of the faces of an object and then calculate the normal vector that comes out of the surface. Secondly, to determine the direction of the electric field of an object, one first need to know the number of dimensions of an object (i.e: 6 faces in a rectangular prism) and areas for each face of the object. Finally, one should be able to calculate the electric flux of an object by multiplying the electric field at a location on each surface of the box by corresponding normal vector and multiplying this value by the area of the surface that was just calculated. One must repeat this process the remaining surfaces (faces) and by adding up all electric flux, that will be the electric flux of the object one wanted to calculate. This value is essential because it will be useful for calculating total charged enclosed inside the object later on. The above written method of calculating electric flux may be confusing at first, but knowing the Gauss's Law, being able to apply this Law to the real problem, and by going through the example below should make sure understanding of this concept.<br />
<br />
== Energy ==<br />
The Gauss's Law simplifies definition of "Electric Flux" into a one simple equation. <br />
<br />
<br />
[[File:Gauss.JPG]]<br />
<br />
<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html Gauss's Law]<br />
<br />
[http://www.colorado.edu/physics/phys1120/phys1120_sp08/notes/notes/Knight27_gauss_lect.pdf Gauss's Law Examples]<br />
<br />
====??====<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
<br />
[[File:BBB.PNG]]<br />
<br />
Electric flux on the disk, by using Gauss's Law, is the multiplication between Electric Field normal to the disk's surface and surface area of the disk.<br />
<br />
Electric Field Normal to the Surface: E x sin(40) = 327 V/m x sin(40)<br />
<br />
Surface Area of the disk: 3.14 x 0.02 x 0.02 m^2<br />
<br />
Electric Flux on the Disk: 327 V/m x sin(40) x 3.14 x 0.02 x 0.02 m^2 = 0.264 Vm<br />
<br />
===Middling===<br />
The electric field has been measured to be vertically upward everywhere on the surface of a box 20 cm long, 4 cm high, and 3 cm deep, shown in the figure. All over the bottom of the box E1 = 1100 V/m, all over the sides E2 = 950 V/m, and all over the top E3 = 750 V/m.<br />
<br />
[[File:sss.JPG]]<br />
<br />
Since E1, E2, and E3, are all measured to be vertically upward everywhere on the surface of a box, only the bottom surface and the top surface will be focused (multiplying the normal vector of other surfaces than the bottom and top surfaces will result in zero electric flux). The normal vector of the bottom surface is known to be <0,-1,0> and that of the top surface is known to be <0,1,0> assuming vertically upward is in +y direction. <br />
<br />
E1 = <0, 1100, 0> V/m,<br />
E2 = <0, 950, 0> V/m,<br />
E3 = <0, 750, 0> V/m,<br />
<br />
E1 corresponds to the bottom surface according to the diagram. Multiplying vector E1 with its normal vector of the bottom surface equals -1100 (dot product), and multiplying this vector by the area equals -1100 V/m x 0.20 m x 0.03 m = -6.6 Vm.<br />
<br />
E3 corresponds to the top surface according to the diagram. Multiplying vector E3 with its normal vector of the top surface equals 750 (dot product) and multiplying this vector by the area equals 750 V/m x 0.20 m x 0.03 m = 4.5 Vm.<br />
<br />
Therefore, the sum of the electric flux in this box equals -6.6 Vm + 4.5 Vm = -2.1 Vm<br />
<br />
To determine the amount of charge enclosed by the box, we use Gauss's Law. Since we know the sum of the electric flux, in order to find q (inside the box) we just have to multiply summed electric flux and epsilon naught (8.85 e-12 unit)<br />
<br />
Total Charge: -2.1 x 8.85 x 10 ^ (-12) = -1.8585 x 10 ^ (-11) C<br />
<br />
===Difficult===<br />
<br />
[[File:AAA.JPG]]<br />
<br />
To calculate the electric flux you will have to know the normal vector or the electric field in normal direction of each side of the cube.<br />
<br />
There are only two sides affecting the net electric flux on this cubical surface, bottom face and right-handed side face (rest will be zero).<br />
<br />
Normal Electric Field (Bottom Face): E1 x sin(27) = 400 V/m x sin(27) x 0.35m x 0.35m = 22.2455 Vm<br />
<br />
Normal Electric Field (Right-Handed Side Face): E1 x sin(27) = 400 V/m x sin(27) x 0.35m x 0.35m = 22.2455 Vm<br />
<br />
Net Electric Field = 44.49 Vm<br />
<br />
Net Charge inside the cubical surface = 44.19 Vm x 8.85 x 10 ^ (-12) = 3.94 x 10 ^ (-10) C<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
<br />
<br />
<br />
#How is it connected to your major?<br />
<br />
I am majoring in Materials Science and Engineering and going further on from Electric Flux, there is a way to calculate Electric Flux Density (D). To obtain D, you have to multiply epsilon (permittivity) of the material to the Electric Field, E. Of course, different materials will have different Electric Flux. For example there are three major types of materials: insulator, semi-conductor, and conductor. Depending on their uses, you would want to make sure that the material of the desired product does not contain electric flux due to excess charge on the surface. This is the reason that electric flux and total charge of the closed surfaced objects are useful when as an engineer you want to think what type of properties you would desire for your product.<br />
<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Thermodynamics was brought up as a science in the 18th and 19th centuries. However, it was first brought up by Galilei, who introduced the concept of temperature and invented the first thermometer. G. Black first introduced the word 'thermodynamics'. Later, G. Wilke introduced another unit of measurement known as the calorie that measures heat. The idea of thermodynamics was brought up by Nicolas Leonard Sadi Carnot. He is often known as "the father of thermodynamics". It all began with the development of the steam engine during the Industrial Revolution. He devised an ideal cycle of operation. During his observations and experimentations, he had the incorrect notion that heat is conserved, however he was able to lay down theorems that led to the development of thermodynamics. In the 20th century, the science of thermodynamics became a conventional term and a basic division of physics. Thermodynamics dealt with the study of general properties of physical systems under equilibrium and the conditions necessary to obtain equilibrium. <br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
[http://www.phys.utk.edu/daunt/EM/PDF/SJDLecture22.pdf Electric Field and Gauss's Law]<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
https://www.grc.nasa.gov/www/k-12/airplane/thermo0.html<br />
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html<br />
https://www.grc.nasa.gov/www/k-12/airplane/thermo2.html<br />
http://www.phys.nthu.edu.tw/~thschang/notes/GP21.pdf<br />
http://www.eoearth.org/view/article/153532/<br />
<br />
[[Category:Interactions]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=4358Simple Harmonic Motion2015-11-30T13:00:36Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
== Introduction ==<br />
<br />
The two major components in Physics II are interactions between electric fields and magnetic fields. This broad subject focuses from a simple topic, electric fields to a much complex idea, electromagnetic radiation. Though this course is very broad in terms of materials that it covers, each topic is very important in understanding the phenomena of electric and magnetic interactions between particles (protons, electrons, dipoles, point charge, capacitor, and, etc), as omitting one concept out of hundreds of concept could lead one approaching the problem differently. This Wiki Page will discuss Chapter 21 of the Matters and Interactions Text Book, 4th edition (Patterns of Field in Space), specifically Gauss's Law and Electric Flux. In order to understand these concepts, one first need to understand the definition of electric field and know each component of Gauss's Law. <br />
<br />
== Dynamics ==<br />
<br />
"Electric Flux" is a quantitative measure of the amount and direction of electric field over an entire surface of a specified object. There are two components in electric flux: direction of the electric field and magnitude of the electric field. These two sums up and give us the value, electric flux, which has a unit of Vm. In order to determine the direction of the electric field of an object, one need to figure out the x,y,z coordinates of the faces of an object and then calculate the normal vector that comes out of the surface. Secondly, to determine the direction of the electric field of an object, one first need to know the number of dimensions of an object (i.e: 6 faces in a rectangular prism) and areas for each face of the object. Finally, one should be able to calculate the electric flux of an object by multiplying the electric field at a location on each surface of the box by corresponding normal vector and multiplying this value by the area of the surface that was just calculated. One must repeat this process the remaining surfaces (faces) and by adding up all electric flux, that will be the electric flux of the object one wanted to calculate. This value is essential because it will be useful for calculating total charged enclosed inside the object later on. The above written method of calculating electric flux may be confusing at first, but knowing the Gauss's Law, being able to apply this Law to the real problem, and by going through the example below should make sure understanding of this concept.<br />
<br />
== Energy ==<br />
The Gauss's Law simplifies definition of "Electric Flux" into a one simple equation. <br />
<br />
<br />
[[File:Gauss.JPG]]<br />
<br />
<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html Gauss's Law]<br />
<br />
[http://www.colorado.edu/physics/phys1120/phys1120_sp08/notes/notes/Knight27_gauss_lect.pdf Gauss's Law Examples]<br />
<br />
====Examples====<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
<br />
[[File:BBB.PNG]]<br />
<br />
Electric flux on the disk, by using Gauss's Law, is the multiplication between Electric Field normal to the disk's surface and surface area of the disk.<br />
<br />
Electric Field Normal to the Surface: E x sin(40) = 327 V/m x sin(40)<br />
<br />
Surface Area of the disk: 3.14 x 0.02 x 0.02 m^2<br />
<br />
Electric Flux on the Disk: 327 V/m x sin(40) x 3.14 x 0.02 x 0.02 m^2 = 0.264 Vm<br />
<br />
===Middling===<br />
The electric field has been measured to be vertically upward everywhere on the surface of a box 20 cm long, 4 cm high, and 3 cm deep, shown in the figure. All over the bottom of the box E1 = 1100 V/m, all over the sides E2 = 950 V/m, and all over the top E3 = 750 V/m.<br />
<br />
[[File:sss.JPG]]<br />
<br />
Since E1, E2, and E3, are all measured to be vertically upward everywhere on the surface of a box, only the bottom surface and the top surface will be focused (multiplying the normal vector of other surfaces than the bottom and top surfaces will result in zero electric flux). The normal vector of the bottom surface is known to be <0,-1,0> and that of the top surface is known to be <0,1,0> assuming vertically upward is in +y direction. <br />
<br />
E1 = <0, 1100, 0> V/m,<br />
E2 = <0, 950, 0> V/m,<br />
E3 = <0, 750, 0> V/m,<br />
<br />
E1 corresponds to the bottom surface according to the diagram. Multiplying vector E1 with its normal vector of the bottom surface equals -1100 (dot product), and multiplying this vector by the area equals -1100 V/m x 0.20 m x 0.03 m = -6.6 Vm.<br />
<br />
E3 corresponds to the top surface according to the diagram. Multiplying vector E3 with its normal vector of the top surface equals 750 (dot product) and multiplying this vector by the area equals 750 V/m x 0.20 m x 0.03 m = 4.5 Vm.<br />
<br />
Therefore, the sum of the electric flux in this box equals -6.6 Vm + 4.5 Vm = -2.1 Vm<br />
<br />
To determine the amount of charge enclosed by the box, we use Gauss's Law. Since we know the sum of the electric flux, in order to find q (inside the box) we just have to multiply summed electric flux and epsilon naught (8.85 e-12 unit)<br />
<br />
Total Charge: -2.1 x 8.85 x 10 ^ (-12) = -1.8585 x 10 ^ (-11) C<br />
<br />
===Difficult===<br />
<br />
[[File:AAA.JPG]]<br />
<br />
To calculate the electric flux you will have to know the normal vector or the electric field in normal direction of each side of the cube.<br />
<br />
There are only two sides affecting the net electric flux on this cubical surface, bottom face and right-handed side face (rest will be zero).<br />
<br />
Normal Electric Field (Bottom Face): E1 x sin(27) = 400 V/m x sin(27) x 0.35m x 0.35m = 22.2455 Vm<br />
<br />
Normal Electric Field (Right-Handed Side Face): E1 x sin(27) = 400 V/m x sin(27) x 0.35m x 0.35m = 22.2455 Vm<br />
<br />
Net Electric Field = 44.49 Vm<br />
<br />
Net Charge inside the cubical surface = 44.19 Vm x 8.85 x 10 ^ (-12) = 3.94 x 10 ^ (-10) C<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
<br />
<br />
<br />
#How is it connected to your major?<br />
<br />
I am majoring in Materials Science and Engineering and going further on from Electric Flux, there is a way to calculate Electric Flux Density (D). To obtain D, you have to multiply epsilon (permittivity) of the material to the Electric Field, E. Of course, different materials will have different Electric Flux. For example there are three major types of materials: insulator, semi-conductor, and conductor. Depending on their uses, you would want to make sure that the material of the desired product does not contain electric flux due to excess charge on the surface. This is the reason that electric flux and total charge of the closed surfaced objects are useful when as an engineer you want to think what type of properties you would desire for your product.<br />
<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Thermodynamics was brought up as a science in the 18th and 19th centuries. However, it was first brought up by Galilei, who introduced the concept of temperature and invented the first thermometer. G. Black first introduced the word 'thermodynamics'. Later, G. Wilke introduced another unit of measurement known as the calorie that measures heat. The idea of thermodynamics was brought up by Nicolas Leonard Sadi Carnot. He is often known as "the father of thermodynamics". It all began with the development of the steam engine during the Industrial Revolution. He devised an ideal cycle of operation. During his observations and experimentations, he had the incorrect notion that heat is conserved, however he was able to lay down theorems that led to the development of thermodynamics. In the 20th century, the science of thermodynamics became a conventional term and a basic division of physics. Thermodynamics dealt with the study of general properties of physical systems under equilibrium and the conditions necessary to obtain equilibrium. <br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
[http://www.phys.utk.edu/daunt/EM/PDF/SJDLecture22.pdf Electric Field and Gauss's Law]<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
https://www.grc.nasa.gov/www/k-12/airplane/thermo0.html<br />
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html<br />
https://www.grc.nasa.gov/www/k-12/airplane/thermo2.html<br />
http://www.phys.nthu.edu.tw/~thschang/notes/GP21.pdf<br />
http://www.eoearth.org/view/article/153532/<br />
<br />
[[Category:Which Category did you place this in?]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=4357Simple Harmonic Motion2015-11-30T12:51:22Z<p>Mmcdaniel: </p>
<hr />
<div>Claimed by Mary Francis McDaniel<br />
<br />
== Patterns of Field in Space ==<br />
<br />
The two major components in Physics II are interactions between electric fields and magnetic fields. This broad subject focuses from a simple topic, electric fields to a much complex idea, electromagnetic radiation. Though this course is very broad in terms of materials that it covers, each topic is very important in understanding the phenomena of electric and magnetic interactions between particles (protons, electrons, dipoles, point charge, capacitor, and, etc), as omitting one concept out of hundreds of concept could lead one approaching the problem differently. This Wiki Page will discuss Chapter 21 of the Matters and Interactions Text Book, 4th edition (Patterns of Field in Space), specifically Gauss's Law and Electric Flux. In order to understand these concepts, one first need to understand the definition of electric field and know each component of Gauss's Law. <br />
<br />
== Electric Flux ==<br />
<br />
"Electric Flux" is a quantitative measure of the amount and direction of electric field over an entire surface of a specified object. There are two components in electric flux: direction of the electric field and magnitude of the electric field. These two sums up and give us the value, electric flux, which has a unit of Vm. In order to determine the direction of the electric field of an object, one need to figure out the x,y,z coordinates of the faces of an object and then calculate the normal vector that comes out of the surface. Secondly, to determine the direction of the electric field of an object, one first need to know the number of dimensions of an object (i.e: 6 faces in a rectangular prism) and areas for each face of the object. Finally, one should be able to calculate the electric flux of an object by multiplying the electric field at a location on each surface of the box by corresponding normal vector and multiplying this value by the area of the surface that was just calculated. One must repeat this process the remaining surfaces (faces) and by adding up all electric flux, that will be the electric flux of the object one wanted to calculate. This value is essential because it will be useful for calculating total charged enclosed inside the object later on. The above written method of calculating electric flux may be confusing at first, but knowing the Gauss's Law, being able to apply this Law to the real problem, and by going through the example below should make sure understanding of this concept.<br />
<br />
== Gauss's Law ==<br />
The Gauss's Law simplifies definition of "Electric Flux" into a one simple equation. <br />
<br />
<br />
[[File:Gauss.JPG]]<br />
<br />
<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html Gauss's Law]<br />
<br />
[http://www.colorado.edu/physics/phys1120/phys1120_sp08/notes/notes/Knight27_gauss_lect.pdf Gauss's Law Examples]<br />
<br />
====A Computational Model====<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
<br />
[[File:BBB.PNG]]<br />
<br />
Electric flux on the disk, by using Gauss's Law, is the multiplication between Electric Field normal to the disk's surface and surface area of the disk.<br />
<br />
Electric Field Normal to the Surface: E x sin(40) = 327 V/m x sin(40)<br />
<br />
Surface Area of the disk: 3.14 x 0.02 x 0.02 m^2<br />
<br />
Electric Flux on the Disk: 327 V/m x sin(40) x 3.14 x 0.02 x 0.02 m^2 = 0.264 Vm<br />
<br />
===Middling===<br />
The electric field has been measured to be vertically upward everywhere on the surface of a box 20 cm long, 4 cm high, and 3 cm deep, shown in the figure. All over the bottom of the box E1 = 1100 V/m, all over the sides E2 = 950 V/m, and all over the top E3 = 750 V/m.<br />
<br />
[[File:sss.JPG]]<br />
<br />
Since E1, E2, and E3, are all measured to be vertically upward everywhere on the surface of a box, only the bottom surface and the top surface will be focused (multiplying the normal vector of other surfaces than the bottom and top surfaces will result in zero electric flux). The normal vector of the bottom surface is known to be <0,-1,0> and that of the top surface is known to be <0,1,0> assuming vertically upward is in +y direction. <br />
<br />
E1 = <0, 1100, 0> V/m,<br />
E2 = <0, 950, 0> V/m,<br />
E3 = <0, 750, 0> V/m,<br />
<br />
E1 corresponds to the bottom surface according to the diagram. Multiplying vector E1 with its normal vector of the bottom surface equals -1100 (dot product), and multiplying this vector by the area equals -1100 V/m x 0.20 m x 0.03 m = -6.6 Vm.<br />
<br />
E3 corresponds to the top surface according to the diagram. Multiplying vector E3 with its normal vector of the top surface equals 750 (dot product) and multiplying this vector by the area equals 750 V/m x 0.20 m x 0.03 m = 4.5 Vm.<br />
<br />
Therefore, the sum of the electric flux in this box equals -6.6 Vm + 4.5 Vm = -2.1 Vm<br />
<br />
To determine the amount of charge enclosed by the box, we use Gauss's Law. Since we know the sum of the electric flux, in order to find q (inside the box) we just have to multiply summed electric flux and epsilon naught (8.85 e-12 unit)<br />
<br />
Total Charge: -2.1 x 8.85 x 10 ^ (-12) = -1.8585 x 10 ^ (-11) C<br />
<br />
===Difficult===<br />
<br />
[[File:AAA.JPG]]<br />
<br />
To calculate the electric flux you will have to know the normal vector or the electric field in normal direction of each side of the cube.<br />
<br />
There are only two sides affecting the net electric flux on this cubical surface, bottom face and right-handed side face (rest will be zero).<br />
<br />
Normal Electric Field (Bottom Face): E1 x sin(27) = 400 V/m x sin(27) x 0.35m x 0.35m = 22.2455 Vm<br />
<br />
Normal Electric Field (Right-Handed Side Face): E1 x sin(27) = 400 V/m x sin(27) x 0.35m x 0.35m = 22.2455 Vm<br />
<br />
Net Electric Field = 44.49 Vm<br />
<br />
Net Charge inside the cubical surface = 44.19 Vm x 8.85 x 10 ^ (-12) = 3.94 x 10 ^ (-10) C<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
<br />
<br />
<br />
#How is it connected to your major?<br />
<br />
I am majoring in Materials Science and Engineering and going further on from Electric Flux, there is a way to calculate Electric Flux Density (D). To obtain D, you have to multiply epsilon (permittivity) of the material to the Electric Field, E. Of course, different materials will have different Electric Flux. For example there are three major types of materials: insulator, semi-conductor, and conductor. Depending on their uses, you would want to make sure that the material of the desired product does not contain electric flux due to excess charge on the surface. This is the reason that electric flux and total charge of the closed surfaced objects are useful when as an engineer you want to think what type of properties you would desire for your product.<br />
<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Thermodynamics was brought up as a science in the 18th and 19th centuries. However, it was first brought up by Galilei, who introduced the concept of temperature and invented the first thermometer. G. Black first introduced the word 'thermodynamics'. Later, G. Wilke introduced another unit of measurement known as the calorie that measures heat. The idea of thermodynamics was brought up by Nicolas Leonard Sadi Carnot. He is often known as "the father of thermodynamics". It all began with the development of the steam engine during the Industrial Revolution. He devised an ideal cycle of operation. During his observations and experimentations, he had the incorrect notion that heat is conserved, however he was able to lay down theorems that led to the development of thermodynamics. In the 20th century, the science of thermodynamics became a conventional term and a basic division of physics. Thermodynamics dealt with the study of general properties of physical systems under equilibrium and the conditions necessary to obtain equilibrium. <br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
[http://www.phys.utk.edu/daunt/EM/PDF/SJDLecture22.pdf Electric Field and Gauss's Law]<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
https://www.grc.nasa.gov/www/k-12/airplane/thermo0.html<br />
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html<br />
https://www.grc.nasa.gov/www/k-12/airplane/thermo2.html<br />
http://www.phys.nthu.edu.tw/~thschang/notes/GP21.pdf<br />
http://www.eoearth.org/view/article/153532/<br />
<br />
[[Category:Which Category did you place this in?]]</div>Mmcdanielhttp://www.physicsbook.gatech.edu/index.php?title=Simple_Harmonic_Motion&diff=4356Simple Harmonic Motion2015-11-30T12:50:02Z<p>Mmcdaniel: </p>
<hr />
<div>Template<br />
Claimed by Mary Francis McDaniel<br />
<br />
Contents [hide] <br />
1 Patterns of Field in Space<br />
2 Electric Flux<br />
3 Gauss's Law<br />
3.1 A Computational Model<br />
4 Examples<br />
4.1 Simple<br />
4.2 Middling<br />
4.3 Difficult<br />
5 Connectedness<br />
6 History<br />
7 See also<br />
7.1 Further reading<br />
7.2 External links<br />
8 References<br />
Patterns of Field in Space[edit]<br />
The two major components in Physics II are interactions between electric fields and magnetic fields. This broad subject focuses from a simple topic, electric fields to a much complex idea, electromagnetic radiation. Though this course is very broad in terms of materials that it covers, each topic is very important in understanding the phenomena of electric and magnetic interactions between particles (protons, electrons, dipoles, point charge, capacitor, and, etc), as omitting one concept out of hundreds of concept could lead one approaching the problem differently. This Wiki Page will discuss Chapter 21 of the Matters and Interactions Text Book, 4th edition (Patterns of Field in Space), specifically Gauss's Law and Electric Flux. In order to understand these concepts, one first need to understand the definition of electric field and know each component of Gauss's Law.<br />
<br />
Electric Flux[edit]<br />
"Electric Flux" is a quantitative measure of the amount and direction of electric field over an entire surface of a specified object. There are two components in electric flux: direction of the electric field and magnitude of the electric field. These two sums up and give us the value, electric flux, which has a unit of Vm. In order to determine the direction of the electric field of an object, one need to figure out the x,y,z coordinates of the faces of an object and then calculate the normal vector that comes out of the surface. Secondly, to determine the direction of the electric field of an object, one first need to know the number of dimensions of an object (i.e: 6 faces in a rectangular prism) and areas for each face of the object. Finally, one should be able to calculate the electric flux of an object by multiplying the electric field at a location on each surface of the box by corresponding normal vector and multiplying this value by the area of the surface that was just calculated. One must repeat this process the remaining surfaces (faces) and by adding up all electric flux, that will be the electric flux of the object one wanted to calculate. This value is essential because it will be useful for calculating total charged enclosed inside the object later on. The above written method of calculating electric flux may be confusing at first, but knowing the Gauss's Law, being able to apply this Law to the real problem, and by going through the example below should make sure understanding of this concept.<br />
<br />
Gauss's Law[edit]<br />
The Gauss's Law simplifies definition of "Electric Flux" into a one simple equation.<br />
<br />
<br />
Gauss.JPG<br />
<br />
<br />
Gauss's Law<br />
<br />
Gauss's Law Examples<br />
<br />
A Computational Model[edit]<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript<br />
<br />
Examples[edit]<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
Simple[edit]<br />
BBB.PNG<br />
<br />
Electric flux on the disk, by using Gauss's Law, is the multiplication between Electric Field normal to the disk's surface and surface area of the disk.<br />
<br />
Electric Field Normal to the Surface: E x sin(40) = 327 V/m x sin(40)<br />
<br />
Surface Area of the disk: 3.14 x 0.02 x 0.02 m^2<br />
<br />
Electric Flux on the Disk: 327 V/m x sin(40) x 3.14 x 0.02 x 0.02 m^2 = 0.264 Vm<br />
<br />
Middling[edit]<br />
The electric field has been measured to be vertically upward everywhere on the surface of a box 20 cm long, 4 cm high, and 3 cm deep, shown in the figure. All over the bottom of the box E1 = 1100 V/m, all over the sides E2 = 950 V/m, and all over the top E3 = 750 V/m.<br />
<br />
Sss.JPG<br />
<br />
Since E1, E2, and E3, are all measured to be vertically upward everywhere on the surface of a box, only the bottom surface and the top surface will be focused (multiplying the normal vector of other surfaces than the bottom and top surfaces will result in zero electric flux). The normal vector of the bottom surface is known to be <0,-1,0> and that of the top surface is known to be <0,1,0> assuming vertically upward is in +y direction.<br />
<br />
E1 = <0, 1100, 0> V/m, E2 = <0, 950, 0> V/m, E3 = <0, 750, 0> V/m,<br />
<br />
E1 corresponds to the bottom surface according to the diagram. Multiplying vector E1 with its normal vector of the bottom surface equals -1100 (dot product), and multiplying this vector by the area equals -1100 V/m x 0.20 m x 0.03 m = -6.6 Vm.<br />
<br />
E3 corresponds to the top surface according to the diagram. Multiplying vector E3 with its normal vector of the top surface equals 750 (dot product) and multiplying this vector by the area equals 750 V/m x 0.20 m x 0.03 m = 4.5 Vm.<br />
<br />
Therefore, the sum of the electric flux in this box equals -6.6 Vm + 4.5 Vm = -2.1 Vm<br />
<br />
To determine the amount of charge enclosed by the box, we use Gauss's Law. Since we know the sum of the electric flux, in order to find q (inside the box) we just have to multiply summed electric flux and epsilon naught (8.85 e-12 unit)<br />
<br />
Total Charge: -2.1 x 8.85 x 10 ^ (-12) = -1.8585 x 10 ^ (-11) C<br />
<br />
Difficult[edit]<br />
AAA.JPG<br />
<br />
To calculate the electric flux you will have to know the normal vector or the electric field in normal direction of each side of the cube.<br />
<br />
There are only two sides affecting the net electric flux on this cubical surface, bottom face and right-handed side face (rest will be zero).<br />
<br />
Normal Electric Field (Bottom Face): E1 x sin(27) = 400 V/m x sin(27) x 0.35m x 0.35m = 22.2455 Vm<br />
<br />
Normal Electric Field (Right-Handed Side Face): E1 x sin(27) = 400 V/m x sin(27) x 0.35m x 0.35m = 22.2455 Vm<br />
<br />
Net Electric Field = 44.49 Vm<br />
<br />
Net Charge inside the cubical surface = 44.19 Vm x 8.85 x 10 ^ (-12) = 3.94 x 10 ^ (-10) C<br />
<br />
Connectedness[edit]<br />
How is this topic connected to something that you are interested in?<br />
<br />
How is it connected to your major?<br />
I am majoring in Materials Science and Engineering and going further on from Electric Flux, there is a way to calculate Electric Flux Density (D). To obtain D, you have to multiply epsilon (permittivity) of the material to the Electric Field, E. Of course, different materials will have different Electric Flux. For example there are three major types of materials: insulator, semi-conductor, and conductor. Depending on their uses, you would want to make sure that the material of the desired product does not contain electric flux due to excess charge on the surface. This is the reason that electric flux and total charge of the closed surfaced objects are useful when as an engineer you want to think what type of properties you would desire for your product.<br />
<br />
Is there an interesting industrial application?<br />
History[edit]<br />
Thermodynamics was brought up as a science in the 18th and 19th centuries. However, it was first brought up by Galilei, who introduced the concept of temperature and invented the first thermometer. G. Black first introduced the word 'thermodynamics'. Later, G. Wilke introduced another unit of measurement known as the calorie that measures heat. The idea of thermodynamics was brought up by Nicolas Leonard Sadi Carnot. He is often known as "the father of thermodynamics". It all began with the development of the steam engine during the Industrial Revolution. He devised an ideal cycle of operation. During his observations and experimentations, he had the incorrect notion that heat is conserved, however he was able to lay down theorems that led to the development of thermodynamics. In the 20th century, the science of thermodynamics became a conventional term and a basic division of physics. Thermodynamics dealt with the study of general properties of physical systems under equilibrium and the conditions necessary to obtain equilibrium.<br />
<br />
See also[edit]<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
Further reading[edit]<br />
Books, Articles or other print media on this topic<br />
<br />
Electric Field and Gauss's Law<br />
<br />
External links[edit]<br />
Internet resources on this topic<br />
<br />
References[edit]<br />
https://www.grc.nasa.gov/www/k-12/airplane/thermo0.html http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html https://www.grc.nasa.gov/www/k-12/airplane/thermo2.html http://www.phys.nthu.edu.tw/~thschang/notes/GP21.pdf http://www.eoearth.org/view/article/153532/<br />
<br />
Category: Interactions</div>Mmcdaniel