A note on the method of harmonic balance

The perturbation methods (the Poincare, the asymptotic and the multiple scale methods) can only be applied to weakly non-linear systems. This well-known remark has been verified in [1] through a comparison between the exact free oscillation period of the Duffing oscillator (1.1) and that given by the Poincare method. The present article deals with the same question but for the asymptotic and the harmonic balance methods; the latter is often used for studying strong non-linear systems although its accuracy needs to be carefully examined. It will be shown that, for large oscillations, the results obtained from the asymptotic method are to be rejected whereas those of the harmonic balance method are acceptable.