Analytic Approach To Investigation of Fluctuation and Frequency of the Oscillatorswith Odd and Even Nonlinearities

This paper we examine fluctuation and frequency of the governing equation of oscillator with odd and even nonlinearities without damping and we present a new efficient modification of the he's homotopy perturbation method for this equation. we applied standard and modified homotopy perturbation method and compare them with the numerical solution (ns), also we applied he's energy balance method (ebm) for study frequency of this equation. by compare modified homotopy perturbation method with numerical solution we find that this modified homotopy perturbation method works very well for the wide range of time and boundary conditions for nonlinear oscillator, and comparison of the result obtained using this method for frequency with those obtained by energy balance method reveals that the former is very effective and convenient. the new modified method accelerates the rapid convergence of the solution, reduces the error solution and increases the validity range for fluctuation and frequency.