Fig. 1

Comparison of the analytical approximate periodic solution obtained by present method (denoting by circles line) with numerical solution obtained by fourth order Runge–Kutta method (denoted by solid line) and also with the first-order (denoted by cross lines) as well as second-order (denoted by dash line) approximations obtained by harmonic balance method (Wu et al. 2003) for \(\alpha = \beta = 1,\,\,A = 10\)