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In this paper, two powerful analytical methods known as modi fie homotopy perturbation method and Amplitude Frequency Formulation called respectively MHPM and AFF, are introduc ed to derive approximate solutions of a system of ordinary di fferential equations appear in mechanical applications. These method s convert a difficult problem into a simple one, which can be ea sily handled. The obtained solutions are compared with numerical fourth o der runge-kutta method to show the applicability and accur a y of both MHPM and AFF in solving this sample problem. The results atta ined in this paper confirm the idea that MHPM and AFF are powerf ul mathematical tools and they can be applied to linear and nonl inear problems.

Application of modified homotopy perturbation method and amplitude frequency formulation to strongly nonlinear oscillators