coupling of energy and harmonic balance method for solving a conservative oscillator with strong odd-nonlinearity

In this paper, a new analytical technique, combining the energy balance method (ebm) with harmonic balance method (hbm), is presented to obtain higherorder approximations of a conservative oscillator with strong oddnonlinearity. to show the accuracy of the present method, one nonlinear oscillator named as cubicquintic duffing oscillator is investigated. the results obtained in this paper are compared with those results determined by other methods and exact solutions. the results give high accuracy and also provide better result than other existing results for both small and large amplitudes of oscillation. the main advantage of the present paper is its simplicity, which contains a few harmonic terms with lower order terms and these terms make the solution quickly converges. the present technique can be used to other nonlinear oscillators.