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In this paper, we investigate two of the analytical approximate techniques, energy balance method and amplitude-frequency formulation, and these approximate techniques are applied to solve the strongly nonlinear differential equation of a mass attached to the center of a stretched elastic wire. We present a comparative study between the energy balance method and amplitude-frequency formulation with exact solution. The approximate results reveal that these methods are very effective and convenient for determining the frequencies of nonlinear dynamical systems.

Determination of the amplitude-frequency for strongly nonlinear oscillator by two approximate analytical techniques