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Freq. of small oscillations in two pendulums

  1. Jul 8, 2009 #1
    1. The problem statement, all variables and given/known data

    Consider two pendulums, I and II. I consists of a bob of mass 2m at the end of a rod of length L. II consists of one bob of mass m at the end of a rod of lenght L and another bob of mass m halfway up the road, at L/2. What is the ratio of the frequency of small oscillations of pendulum II to that of pendulum I?

    2. Relevant equations

    As far as I know, for small oscillations, the frequency is given by sqrt(g/L), where g is the acceleration of gravity, and L is the length of the pendulum. Therefore, the frequency of small oscillations is proportional to sqrt(1/L).

    3. The attempt at a solution

    if wII is the frequency for pendulum II and LII is the length of pendulum II, and wI is the frequency for pendulum I and LI is the length of pendulum I:

    wII/wI = sqrt(1/LII)/sqrt(1/LI)

    As I understand it, for an ideal pendulum, L refers to the position of the bob. The way I saw it, the "Bob" of pendulum II is located at the center of mass of the two Bobs. since one is at L and the other is at L/2, the center of mass is at 3L/4. Therefore:

    wII/wI = sqrt(4/3)/sqrt(1/1) = sqrt(4/3)

    However, the answer is actually sqrt(6/5) !!! Any Ideas?
     
  2. jcsd
  3. Jul 8, 2009 #2

    LowlyPion

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    Maybe consider the frequency of a compound pendulum.

    f = (m*g*L / I)1/2/ (2 * π)

    Aren't you going to want to be interested in the moment of inertia and not just the center of mass?

    Edit: as davieddy points out the L in this case is the distance to the center of mass
     
    Last edited: Jul 8, 2009
  4. Jul 8, 2009 #3
    L (in your formula) is the distance of the center of mass from the pivot,
    not the L specified in the question.
     
  5. Jul 8, 2009 #4

    LowlyPion

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    Thanks for the clarification.
     
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