Classical Dynamics of Particles and Systems · Problem 3-10

Nonlinear Oscillations and Chaos — Marion & Thornton

Physics — Mechanics · damped-oscillator-frequency

Problem

If the amplitude of a damped oscillator decreases to

1/e

of its initial value after

n

periods, show that the frequency of the oscillator must be approximately

[1 - (8\pi^2 n^2)^{-1}]

times the frequency of the corresponding undamped oscillator.