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Homework Help: Calling all pendulum experts

  1. Nov 27, 2004 #1
    I have no idea what the Q factor is in the following problem:

    Consider a simple pendulum (point mass bob) 0.50 m long with a Q of 400.

    How long does it take for the amplitude (assumed small) to decrease by two-thirds?

    If the amplitude is 3.0 cm and the bob has mass 0.20 kg, what is the initial energy loss rate of the pendulum in watts? (The answer should have a negtive sign.)

    If we are to stimultate resonance with a sinusoidal driving force, how close must the driving frequency be to the natural frequency of the pendulum?
     
  2. jcsd
  3. Nov 28, 2004 #2

    Tide

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    Q is the "quality factor" and is a measure of the energy loss per cycle:

    [tex]Q = \omega \left| \frac {E}{\Delta E} \right|[/tex]

    Low Q means high damping and high Q means low dampiing. You should be able to take it from there!
     
  4. Nov 29, 2004 #3
    How is the angular frequency related to amplitude and energy?
     
  5. Nov 30, 2004 #4

    Tide

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    The angular frequency is related to the length of the pendulum:

    [tex]\omega = \sqrt \frac {g}{L}[/tex]

    and the amplitude will look something like

    [tex]x = x_0 \cos \omega t[/tex]

    from which you can calculate the velocity and kinetic energy (and you can also obtain the potential energy).
     
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