Classical Mechanics (Kibble & Berkshire) · Problem 8.13

The energy principle — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · driven-nonlinear-oscillations-perturbation

Problem

A driven non-linear oscillator satisfies the equation x¨+ϵx˙3+x=cos⁡pt,\ddot{x} + \epsilon \dot{x}^3 + x = \cos pt, where ϵ\epsilon, pp are positive constants. Use perturbation theory to find a two-term approximation to the driven response when ϵ\epsilon is small. Are there any restrictions on the value of pp?

Related theory

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