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Pendulum Oscillation

  1. Sep 27, 2009 #1
    1. The problem statement, all variables and given/known data

    A grandfather clock has a pendulum length of 0.7 m and a mass bob of 0.4 kg. A mass
    of 2 kg falls 0.8 m in seven days, providing the energy necessary to keep the amplitude
    (from equilibrium) of the pendulum oscillation steady at 0.03 rad. What is the Q of the
    system?

    2. Relevant equations

    1) Q = [tex]\omega[/tex]R/2[tex]\beta[/tex]

    2) Q = [tex]\omega[/tex]0/[tex]\Delta[/tex][tex]\omega[/tex]

    3. The attempt at a solution

    I figured only equation 1 would help me here, and I can re-arrange it as follows:

    [tex]\beta[/tex] = b/2m (b = damping coefficient)

    Then Q = m[tex]\omega[/tex]R/b

    when amplitude D is a maximum, we can differenciate wrt [tex]\omega[/tex] to obtain maximum (i.e [tex]\omega[/tex]R)

    [tex]\omega[/tex]R = sqrt([tex]\omega[/tex]20 - 2[tex]\beta[/tex]2)

    re-arranging yields

    Q = m sqrt([tex]\omega[/tex]20 - b2/2m2)/b

    I'm kind of stuck because I don't know how to find the coefficient of damping b. Did I go in the wrong direction here? I know I have to use the information given about the pendulum dropping to find the flaw in the system, any help please?
     
  2. jcsd
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