This paper deals with Approximate Analytical Solutions to nonlinear oscillations of a conservative, non-natural, single-degreeof- freedom system with odd nonlinearity. By extending the Variational approach proposed by He, we established approximate analytical formulas for the period and periodic solution.To illustrate the applicability and accuracy of the method, two examples are presented: (i) the motion of a rigid rod rocking back and forth on the circular surface without slipping, and (ii) Cubic-Quintic Duffing Oscillators. Comparison of the result which is obtained by this method with the obtained result by the Exact solution reveals that the He's Variational approach is very effective and convenient and can be easily extended to other nonlinear systems and can therefore be found widely applicable in engineering and other sciences.
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