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Clock Oscillation

  1. Sep 26, 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
  3. Sep 27, 2009 #2

    Redbelly98

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    Staff Emeritus
    Science Advisor
    Homework Helper

    While I'm not certain how to solve the problem, the 2 kg mass dropping tells us at what rate energy is added to the pendulum to overcome damping.

    Also, the power dissipated due to damping is definitely related to b. If you can express that power in terms of b, you should be in good shape.
     
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