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The study of nonlinear oscillators equations is of great importance not only in all areas of physics but also in engineering and other disciplines, since most phenomena in our word are nonlinear and are described by nonlinear equations. Recently, considerable attention has been direct towards the analytical solutions for nonlinear oscillators, for example, elliptic homotopy averaging method, amplitude-frequency formulation, homotopy perturbation method, parameter-expanding method, energy balance method, and others. The aim of this thesis is to study the periodic solutions for some physical systems which the mathematical formulation of these systems leads to a certain set of nonlinear ordinary differential equations of the second order.