Vibrations and Waves · Problem 4-10

Coupled oscillators and normal modes — A.P. French

Physics — Waves · power-input-forced-oscillations

Problem

The power input to maintain forced vibrations can be calculated by recognizing that this power is the mean rate of doing work against the resistive force

-bv

. (a) Satisfy yourself that the instantaneous rate of doing work against this force is equal to

bv^2

. (b) Using

x = A\cos(\omega t - \delta)

, show that the mean rate of doing work is

b\omega^2 A^2/2

. (c) Substitute the value of

A

at any arbitrary frequency and hence obtain the expression for

\bar{P}

as given in Eq. (4-23).

Related theory

Power In Ac Circuits And Power Factor

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