A novel technique to obtain a time-delayed vibration control analytical solution with simulation of He's formula

The impetus for the current investigation relates to the implementation of an efficient novel technique to obtain a time-delayed vibration control analytical solution. The current technique follows simple and easy-to-apply criteria. This technique is based on converting the nonlinear time-delayed Van der Pol (VDP)-Duffing oscillator to an equivalent linear one. Details of the conversion to an equivalent linear ordinary differential equation are mentioned. The convergence between the numerical outcomes and the analytic solution is achieved and gives a satisfying accuracy of the equivalent result.