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Energy loss of damped oscillator

  1. Oct 2, 2005 #1

    I do not know how to drive an experession for energy loss of damped oscillator.I know that:

    X(t)=A exp(-Beta*t)cos(wt-delta)
    I found E=K+U
    but it seems to be so messy. It is like:

    E=(1/2)*m*(A^2)*exp(-2*beta*t)[ beta^2 (cos(wt-delta))^2)+beta*

    sin 2(wt-delta)+w^2 ]

    I do not know if it is right or not but also I do not know how to get the energy loss from it.

    I will thank for help.
  2. jcsd
  3. Oct 3, 2005 #2


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    Science Advisor

    Do you want loss, or loss rate? Loss rate is easy. dE/dt is proportional to v^2. Integrating results indeed in a complicated expression. But if you are in an underdamped regime (many oscillations before the movement decays away), the expression represents an exponential decay with a small modulation on top of it. If you are not interested in the small modulation, the expression is very simple. You can find it for example by finding 1/2 mv^2 at those times when x goes through zero.
  4. Oct 3, 2005 #3
    Finally solved it.
    Thanks for help.
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