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Damped harmonic motion

  1. Oct 20, 2009 #1
    1. The problem statement, all variables and given/known data

    A damped harmonic oscillator has mass m , spring constant k , damping force
    - cv .

    (a) Find the ratio of two successive maxima of the oscillations.

    (b) If the oscillator has Q = 100 , how many periods will it take for the amplitude to decay to 1/ e
    of it’s initial value? What fraction of the initial energy the oscillator has left by this time?

    2. Relevant equations




    3. The attempt at a solution

    Okay, so for a)

    T_d=2pi/omega_d = 2pi/(omega_0^2 - gamma^2)

    The ratio is equal to e^-(gamma * T_d)

    so r = e^-(c/2m * 2pi/(k/m - (c/2m)^2)^1/2)

    But then for b, I'm lost again.

    If Q = 100, omega_d=200*gamma.

    So the ratio of successive maxima = e ^ - pi/100

    But i'm not sure how that lets me figure out how many periods will it take for the amplitude to decay to 1/ e of it’s initial value.
     
  2. jcsd
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