Question

The displacement of a forced oscillator is zero at t = 0 and its rate of growth is governed by the rate of
decay of the transient term. If this term decays to e^−k of its original value in a time t, show that, for small
damping, the average of growth of the oscillations is given by x0/t = F0/2kmω0 where x0 is the maximum
steady state displacement, F0 is the force amplitude and ω0 is the natural frequency.

Answer 1

Answer:

Explanation:

The displacement of a forced oscillator is zero at t = 0 and its rate of growth is governed by the rate of

decay of the transient term. If this term decays to e^−k of its original value in a time t, show that, for small

damping, the average of growth of the oscillations is given by x0/t = F0/2kmω0 where x0 is the maximum

steady state displacement, F0 is the force amplitude and ω0 is the natural frequency.