The approximate solution of a classical quartic anharmonic oscillator with periodic force: a simple analytical approach

The approximate analytical solution of a classical quartic anharmonic oscillator with periodic forcing is obtained by using a complete analytical approach. The present approach starts with a trial solution of time dependent parameters. The trial solution is guessed from the knowledge of the perturbation theory. Finally, the time dependent parameters in the trial solution are found by using appropriate initial conditions. In the limiting situations, the present approach gives rise to the standard (earlier) results. The solution presented in this paper has a great deal of academic interests. The removal of secular terms and the small divisor terms are carefully discussed. It is found that the small divisor terms involving harmonic and subharmonic terms are removed automatically from the solution. However, the removal of terms involving fundamental frequency requires standard methods.