(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Assuming Earth to be a solid sphere, show that if a straight hole were drilled from pole to pole that a particel dropped would undergo simple harmonic motion. Show that the period of the oscillation depends only on the Earth's density and is independent of size. What is the period in hours?

2. Relevant equations

We have already done studying oscillations and this questions mainly pertains to central forces. The obvious equation I have in mind is F = GMm/(r^2) and I know somehow I have to do something that will lead to d^{2}x/dt^{2}= constant*x

3. The attempt at a solution

Something tells me this problem is extremely simple. But I don't understand how to do it. I've reached a bit of a dead end. The equation for the force that is exterted on the particle doesn't display shm.

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# Simple harmonic motion and central forces.

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