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Energy of an damped/undriven oscillator in terms of time?

  1. Oct 16, 2011 #1
    1. The problem statement, all variables and given/known data

    The Q asks to show that the time rate of change in mechanical energy for a damped, undriven oscillator is dE/dt=-bV^2.

    2. Relevant equations

    I assume you take the derivative of the total E eq, E=(1/2)mV^2 + (1/2)kx^2 but I'm unsure how to put the E eq into terms of t, like E(t).

    3. The attempt at a solution

    Would you have to punch in the pos eq [x(t)=(Ae^(-βt))cos(ωt-δ)] in for x, then its derivative in for V? and then takes that entire eq's derivative? Seems like it would be too much work and not enough concept.
    Last edited: Oct 16, 2011
  2. jcsd
  3. Oct 16, 2011 #2
    i cant seem to get it in the form dE/dt=-bV^2.
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