In this paper, a novel analytical approximation for the period and periodic solutions for the Helmholtz-Duffing oscillator is presented. The main idea of present work is to approximate the integration in exact analytical period of equation using a well-known quadrature rules. This approach gives us not only the accurate period of motion but also a truly periodic solution in a rational form as a function of the amplitude of oscillation. Comparison of the result obtained using this approach with the exact one and existing results reveals that the high accurate, simplicity and efficiency of the proposed procedure for the whole range of initial amplitudes and the equation parameter in a variety of cases. The method can be easily extended to other strongly nonlinear oscillators.
