Coupled oscillators and normal modes — A.P. French
Physics — Waves · damped-forced-oscillations
Problem
An object of mass 0.2 kg is hung from a spring whose spring constant is 80 N/m. The body is subject to a resistive force given by −bv, where v is its velocity (m/sec) and b=4 N-m−1 sec.
(a) Set up the differential equation of motion for free oscillations of the system, and find the period of such oscillations.
(b) The object is subjected to a sinusoidal driving force given by F(t)=F0sinωt, where F0=2 N and ω=30 sec−1. In the steady state, what is the amplitude of the forced oscillation?