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For what value of d is the frequency of small oscillations largest?

  1. Dec 13, 2006 #1
    1. The problem statement, all variables and given/known data
    A coin of radius R is pivoted at a point that is distance d from the center. The coin is free to swing back and forth in the vertical plane defined by the plane of the coin. For what value of d is the frequency of small oscillations largest?



    2. Relevant equations

    Frequency = 1/T = (1/2(pi))(k/m)^1/2

    x = A cos( (omega)(t) + phi )



    3. The attempt at a solution

    I assume I have to find some derivative in order to maximize the value, just don't know where to start.
     
  2. jcsd
  3. Dec 13, 2006 #2
    Add on:

    Would this be correct?

    F = ma in the tangental direction

    -mg sin(theta) = ma

    -mg sin(theta) = m((R+d) theta '' ) (note theta '' is 2nd derivative)

    thus omega = (g/(R+d))^1/2

    Or is this totally the wrong idea?
     
  4. Dec 14, 2006 #3

    Meir Achuz

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    Science Advisor
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    Gold Member

    You have to use the moment of inertia of a disk, and then use the parallel axis theorem so that you can apply torque=I alpha to the coin.
     
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