Modified Krylov-Bogoliubov-Mitropolskii method for solving damped nonlinear oscillators

In the recent past, a simplified solution was obtained by using a modified Krylov-Bogoliubov-Mitropolskii method for a cubic Duffing oscillator in the presence of a linear damped force. However, a similar solution is not always possible for another class of nonlinear oscillators where the inertia type force is involved in the nonlinear function along with the restoring forces and in the presence of linear damping. In this paper, an alternative modification of the Krylov-Bogoliubov-Mitropolskii method is introduced to overcome this limitation. The approximated solutions are achieved and comparison with the fourth-order Runge-Kutta method which are represented graphically. The comparison reveals excellent consistency between them.