Simple Harmonic Motion on a Uniform Meter Stick

AI Thread Summary
A uniform meter stick is pivoted at one end and held horizontal by a spring, leading to oscillations that need to be analyzed for frequency. The relevant equations include torque, force, and the relationship between frequency and spring constant. The textbook solution indicates the frequency is (1/2π)√(3k/m). The discussion emphasizes the importance of creating a force diagram and understanding the torque balance at equilibrium and during displacement. The user seeks guidance on progressing from their calculations involving angular acceleration and torque.
NathanLeduc1
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Homework Statement


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?


Homework Equations


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

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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Hi NathanLeduc1! :smile:
NathanLeduc1 said:
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. :wink:

(assume sinx = x)
 
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.
 
(just got up :zzz:)
NathanLeduc1 said:
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 :wink:
 

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