Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook