Classical Mechanics (Kibble & Berkshire) · Problem 8.2

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

Physics — Mechanics · lindstedt-method-nonlinear-oscillations

Problem

A non-linear oscillator satisfies the equation x¨+x+ϵx5=0,\ddot{x} + x + \epsilon x^5 = 0, where ϵ\epsilon is a small parameter. Use Lindstedt's method to obtain a two-term approximation to the oscillation frequency when the oscillation has unit amplitude. [You will need the identity 16cos⁡5s=10cos⁡s+5cos⁡3s+cos⁡5s16\cos^5 s = 10\cos s + 5\cos 3s + \cos 5s.]

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