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Simple Harmonic Motion on a Uniform Meter Stick

  1. May 4, 2013 #1
    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)
     
  2. jcsd
  3. May 4, 2013 #2

    tiny-tim

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    Hi NathanLeduc1! :smile:
    Draw a force diagram for a small vertical displacement x, and find the force as a function of x. :wink:

    (assume sinx = x)
     
  4. May 4, 2013 #3
    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.
     
  5. May 5, 2013 #4

    tiny-tim

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    (just got up :zzz:)
    α = x''/l :wink:
     
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