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The study of nonlinear oscillations has occupied researchers for quite a long period of time.Various perturbation methods such as multiple scales method.Lindstedt-Poincaré method, harmonic balance method and Krylov-Bogoliubov-Mitropolsky (KBM) method have been developed to analysis nonlinear systems[1].ln 1996,A.Maccari[2-4] proposed a reasonably simple analytical method for the study of nonlinear systems.The asymptotic perturbation (AP) method provides a systematic means to obtain increasingly accurate solution by increasing the order of approximation in terms of the small parameter.