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Damped oscillator!

  1. Feb 24, 2006 #1
    I am really struggling with this question...:yuck:

    Question: Consider a damped oscillator, with natural frequency w_0 (omega_0) and damping constant B (beta) both fixed, that is driven by a force F(t)= F_0*cos(wt). Find the rate P(t) at which F(t) does work and show that the average < P > over any number of complete cycles is mBw^2*A^2.

    any help would be amazing!!
  2. jcsd
  3. Feb 24, 2006 #2


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    I think the rules here stipulate that you need to show some of your own work before you can get specific help on homework problems.
  4. Feb 24, 2006 #3

    F(t)=m*f_0*cos(wt) in general
    long term motion x(t)=A*cos(wt-delta)
    delta= arctan((2Bw)/(w_0^2-w^2))
    A^2= (f_0^2)/((w_0^2-w^2)^2+4*B^2*w^2)

    < P >=mBw^2*A^2
    = m*f_0*cos(wt)*distance

    mBw^2*A^2 = mBw^2*(f_0^2)/((w_0^2-w^2)^2+4*B^2*w^2) = m*f_0*cos(wt)*distance

    cancel stuff...

    B*w^2*(f_0)/((w_0^2-w^2)^2+4*B^2*w^2) = cos(wt)*distance

    uh......help? :uhh:
  5. Feb 24, 2006 #4


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    To calculuate the average power over a period you need to evaluate the integral

    [tex]<P> = \frac {1}{T} \int_0^T F v dt[/tex]
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