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Decadohedron

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## Homework Statement

A bead slides along a frictionless wire which lies in the N/S direction, midpoint at the equator. All points along the wire are the same distance from the center of the earth. The bead is initially at rest then released a small distance, δ, to the north of the equator. Because of effective g doesn't point directly towards the Earth's center, there is a small component along the wire that always points back towards the equator. This means that when released, the bead will oscillate back and forth just like a mass on a spring. What is the period of these oscillations?

## Homework Equations

Coriolis force would be 0 as the bead is fixed on a wire, and the centrifugal force would be the force always pointing it back towards the equator - thus the formula being

1.

-GMm/r

^{2}+ mω

^{2}r = 0

2.

T = 2π√(m/k); ω

^{2}=m/k

## The Attempt at a Solution

I was going to solve for ω and then just plug into the Period formula of the mass-spring system. But it seems overly simple and feels like I'm missing something.

Am I on the right track or should I be thinking about this differently??

Thanks.