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swuster
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Homework Statement
The instantaneous power dissipated by the damping force in a driven oscillator is [tex]P(t) = f_x v_x = -bv_x ^2[/tex].
Show that the average power dissipated during one cycle of steady-state motion is [tex]\overline{P} = -\frac{1}{2} b\omega^2 A^2[/tex], where [tex]\omega[/tex] is the driving frequency and [tex]A = |\underline{A}|[/tex] is the oscillation amplitude.
Homework Equations
n/a
The Attempt at a Solution
I'm attempting to just solve an integral for the average power:
[tex] \omega/2\pi*\int^{2\pi/\omega}_{0} -bv_x^2 dt[/tex]
But what is [tex]v_x[/tex]? If [tex]x(t) = \underline{A} e^{i \omega t}[/tex], then [tex]v(t) = i \omega \underline{A} e^{i \omega t} = i\omega x(t)[/tex]. So then I think that [tex]v_x = i\omega[/tex] but this doesn't give me the correct answer when put into the integral. Thanks for the help!
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