• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Simple Harmonic Motion on a Uniform Meter Stick

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)
 

tiny-tim

Science Advisor
Homework Helper
25,790
242
Hi NathanLeduc1! :smile:
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.
 

tiny-tim

Science Advisor
Homework Helper
25,790
242
(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 :wink:
 

Want to reply to this thread?

"Simple Harmonic Motion on a Uniform Meter Stick" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top