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Homework Help: Damping Oscillation

  1. Jan 14, 2009 #1
    1. The problem statement, all variables and given/known data
    A small earthquake starts a lamppost vibrating back and forth. The amplitude of the vibration of the top of the lamppost is 6.5 cm at the moment the quake stops, and 8.0s later it is 1.8 cm.

    What was the time constant for the damping of oscillation?

    What's the amplitude of oscillation after 4.0s after the quake stopped?

    2. Relevant equations

    A = e^(-t/t)

    3. The attempt at a solution

    Professor is the worst, she went over the equation but didn't let us know what the variables stand for.

    Can someone point me in the right direction? it's probably plug and play, but I won't know since I've never done it or seen it
  2. jcsd
  3. Jan 16, 2009 #2
    If the oscillation obeys the equation of the damped harmonic oscillator (which we can assume I guess, since they dont teach fourth order partial differential equations in high school...),
    Then we know that the amplitude decays exponentialy.

    So say, the amplitude at time [tex]t_1[/tex] is [tex]A_1[/tex] ant the amplitude at time [tex]t_2>t_1[/tex] is [tex]A_2[/tex], then the relationship between them is:

    [tex]\frac{A_2}{A_1}=e^{-\beta (t_2-t_1)}[/tex]

    since you know the amplitudes, at two time values, you can calculate the [tex]\beta[/tex] damping coefficient from here, and then everything else...:D
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