I am working on a problem that has a few angles of approach. Im hoping to get at least that right before I waste too much more time. The problem is a slender, uniform, rigid rod is placed to pivot on its center, so that the rotation is taking place at the ends of the rod.(adsbygoogle = window.adsbygoogle || []).push({});

then a spring is attached to the bottom. small angle approximation allowed. initial displacement is [itex]\theta[/itex]

We are to show [itex]\frac{d^2\theta}{dt^2} = -\omega^2\theta[/itex] and [itex]T = \frac{2\pi}{\omega}[/itex] and show how those imply SHM.

My problem is in setting up the equations. I was going to show that the rotational kinetic energy plus the spring potential energy was a constant... but Im guessing after working on it that approach isnt the best.. Any tips?

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# Homework Help: Periodic Motion SHM proof

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