1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
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- graphical interpretation

  1. Oct 13, 2012 #1
    The damped oscillator equation is as follows:
    x(t)= A exp(γt/2) cos(ωt)

    where ω= √( (w0)^2 + (γ^2)/4 )

    I have attached a graph of a damped oscillator.
    The question is if I use graph to measure angular frequency, will it be w0 or ω?

    It should be w0 because if I put γ=0, I should be getting the normal undamped system. The enveloped curve would disappear since exp(γt/2) is 1. BUT then where is ω on the graph!!!! :grumpy:

    Attached Files:

  2. jcsd
  3. Oct 13, 2012 #2


    User Avatar
    Gold Member

    How can u expect ω in an x-t graph? You will have to calculate.
  4. Oct 13, 2012 #3
    of course I know that. Let m rephrase. The time T between successive maxima is constant. So I consider the complete oscillations, k, for a given time, t. To get angular frequency, W= k* 2pi/t
    The question is, what is this this W? is it w0 or is it the angular frequency ω of the damped oscillator
  5. Oct 13, 2012 #4
    it is the angular frequency of damped oscillator.
  6. Oct 13, 2012 #5

    Philip Wood

    User Avatar
    Gold Member

    The answer to your question is ω. Peaks in the damped sinusoid [itex]e^{-kx} cos(\omega t)[/itex]occur a little before the peaks in the pure sinusoid [itex]cos(\omega t)[/itex], but by the same amount each time, so the time between peaks is the same as that between the peaks in [itex]cos(\omega t)[/itex].
  7. Oct 13, 2012 #6


    User Avatar
    Science Advisor
    Homework Helper

    An easier way to see the anwer is ##\omega## is to think about the times when x(t) = 0. They are the roots of ##\cos \omega t = 0##.
  8. Oct 13, 2012 #7

    Philip Wood

    User Avatar
    Gold Member

    AlephZero. Agree, but thought rsaad (in post 3) was worried about maxima.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook