Vibrations and Waves · Problem 4-11

Coupled oscillators and normal modes — A.P. French

Physics — Waves · forced-oscillations-numerical

Problem

Consider a damped oscillator with

m = 0.2

kg,

b = 4

N-m

^{-1}

sec and

k = 80

N/m. Suppose that this oscillator is driven by a force

F = F_0 \cos \omega t

, where

F_0 = 2

N and

\omega = 30

sec

^{-1}

. (a) What are the values

A

and

\delta

of the steady-state response described by

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

? (b) How much energy is dissipated against the resistive force in one cycle? (c) What is the mean power input?