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Problem/CM-01006 Periodic Motion

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Question: Show that the time period of a relativistic oscillator as  function of amplitude $a$ is given by $$ T\approx \frac{2\pi}{\omega}\left[ 1 + \frac{3\omega^2a^2}{16 c^2} + \cdots \right] $$ where the restoring force is $- kx$ and $k=m \omega2 $.

cm-que-01006

 

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