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

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


    User Avatar
    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Energy loss of damped oscillator
  1. Damped Oscillation (Replies: 5)