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phy131studiof15:lectures:chapter16 [2015/07/22 11:02]
mdawber [Simple harmonic motion with multiple springs]
phy131studiof15:lectures:chapter16 [2015/10/31 12:15] (current)
mdawber [Energy in SHM]
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 {{shmvspring.png}} {{shmvspring.png}}
  
 +When the system is in equilibrium
 +
 +$kx_{0}=mg$
 +
 +so 
 +
 +$x_{0}=\frac{mg}{k}$
 ===== SHM as a function of time ===== ===== SHM as a function of time =====
  
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 $T=2\pi\sqrt{\frac{m}{k}}$ ​ $T=2\pi\sqrt{\frac{m}{k}}$ ​
 +
 +===== 16.P.003 =====
 +
 +===== 16.P.008 =====
 +
 +===== 16.P.021 =====
 +
 +
 +
  
 ===== Energy in SHM ===== ===== Energy in SHM =====
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 $v=\pm\sqrt{\frac{k}{m}(A^{2}-x^{2})}$ $v=\pm\sqrt{\frac{k}{m}(A^{2}-x^{2})}$
 +
 +===== 16.P.044 =====
  
 ===== Simple harmonic motion with multiple springs ===== ===== Simple harmonic motion with multiple springs =====
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-===== vertical spring =====+===== Energy for the vertical spring =====
  
 A vertical spring will also execute simple harmonic motion, though it's mean position will be modified by the balance of the gravitational force and the spring force. A vertical spring will also execute simple harmonic motion, though it's mean position will be modified by the balance of the gravitational force and the spring force.
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 [[https://​www.youtube.com/​watch?​v=kBqjbZeAN9g|Video of many carefully arranged pendula]] [[https://​www.youtube.com/​watch?​v=kBqjbZeAN9g|Video of many carefully arranged pendula]]
 +
 +===== 16.P.029 =====
  
  
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