Simple Harmonic Motion on a Uniform Meter Stick

NathanLeduc1

1. The problem statement, all variables and given/known data
A uniform meter stick of mass M is pivoted on a hinge at one end and held horizontal by a spring with spring constant k attached at the other end. If the stick oscillates up and down slightly, what is its frequency?

2. Relevant equations
τ=rFsinθ
f=(1/2π)√(k/m)
F=kx
x=Acos(ωt)

3. The attempt at a solution
I'm really not sure how to get started on this one. If you could just provide me with a little start, I might be able to figure it out. Thanks.

The answer, according to the textbook, is (1/2π)sqrt(3k/m)

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tiny-tim

Homework Helper
Hi NathanLeduc1! If you could just provide me with a little start, I might be able to figure it out.
Draw a force diagram for a small vertical displacement x, and find the force as a function of x. (assume sinx = x)

NathanLeduc1

Ok, so I set up a force diagram and did the following work but I'm stuck again...

At equilibrium:
Ʃτ=Kxol-mg(l/2)=0

After it's been stretched:
Ʃτ=K(x+xo)-mg(l/2)=Iα

This then simplifies to:
Iα=kxol

I wrote α as the second derivative of θ with respect to time but now I'm stuck. Where should I go from here? Thanks.

tiny-tim

Homework Helper
(just got up :zzz:)
Iα=kxol

I wrote α as the second derivative of θ with respect to time but now I'm stuck. Where should I go from here? Thanks.
α = x''/l "Simple Harmonic Motion on a Uniform Meter Stick"

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