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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/r2 + mω2r = 0
2.
T = 2π√(m/k); ω2=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.