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Vibration of double pendulum

  1. Apr 16, 2016 #1
    1. The problem statement, all variables and given/known data
    m = 1 kg, l = 1 m, theta 1 and 2 are small

    I want to work out the natural frequencies (2) of this 2 DOF system through taking torques about the fixed point on the ceiling. I've done it using numerous fixed points and just cannot get the right answer.

    upload_2016-4-16_13-56-58.png

    2. Relevant equations
    sum of torques = I . alpha

    3. The attempt at a solution
    Taking that cos theta = 1 and sin theta or tan theta = theta and acw moments are pos,

    I get that for the lowest mass:
    -mg (theta 2 + theta 1) + T2(theta1 + theta 2) - 2T2theta2 = 4alpha

    for highest mass: -mgtheta1 - T2theta1 + theta2T2 = alpha.

    Does anyone else get this? I want to solve it via torques and not any other method. NB: T2 = tension in lowest massless string.
     
  2. jcsd
  3. Apr 16, 2016 #2

    ehild

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    Gold Member

    This equation is valid for a rigid body. Your system is not that, its parts move with relative to each other. The moment of inertia with respect the fixed point at the ceiling changes during the motion. Draw the FBD-s for both masses, and derive the accelerations in terms of the angles.
     
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