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Homework Help: Damped oscillator consecutive amplitude ratio

  1. Dec 11, 2011 #1
    1. The problem statement, all variables and given/known data
    Undamped oscillator's period [itex]T_0 = 12s[/itex]. Damped oscillator's angular frequency [itex]\omega_1 = \omega_0 * 97\%[/itex] where [itex]\omega_0[/itex] is the angular frequency of the undamped oscillator's. What is the ratio of consecutive maximum amplitudes?

    2. Relevant equations
    Equation of damped oscillator's motion:
    [itex]x = e^{-\alpha t}A_0sin(\omega_1 t + \phi)[/itex]
    where [itex]\alpha = \frac{b}{2m}[/itex] where [itex]b = [/itex]damping constant.

    3. The attempt at a solution
    Firstly, were' talking about maximums so we can disregard the sin() function.
    Calculating [itex]\omega_1 = \omega_0 * 0.97 = \frac{2\pi}{T_0}0.97[/itex].
    Thus for the damped oscillator [itex]T_1 = \frac{T_0}{0.97}[/itex]

    Then we could write something as follows:
    [itex]\frac{x_0}{x_1} = \frac{e^{-\alpha t_0}A_0}{e^{-\alpha t_1}A_0}[/itex]
    but we have no clue of alpha nor about x_0 and x_1... Any help appreciated.
  2. jcsd
  3. Dec 11, 2011 #2
  4. Dec 11, 2011 #3
    I ended up using the formula

    [itex]\zeta = \sqrt{1-(\frac{\omega_1}{\omega_0})^2}[/itex]
    And got approx 0.243 out of it. In my answer spreadsheet they claim the answer to be 0.21 however. Now i'm wondering whether i got it right or not... heh :) Thanks for the help either way.
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