In this paper, a new and innovative semi-analytical technique, namely AkbariGanji\\\\\\\'s Method (AGM), is employed for solving three nonlinear damped oscillatory systems. Applying this method to nonlinear problems is very simple because, in the solving process of only a trial solution, the main dierential equation and its derivatives are required. The analytical solutions obtained by AGM are utilized to study the impact of amplitude on nonlinear frequency and damping ratio. It is found that AGM produces acceptable results for the problems considered in this paper. Moreover, in order to obtain a more accurate solution, instead of using a trial solution with higher-order terms that may result in complicated and time-consuming mathematical calculations, the solution obtained by AGM is improved via Variational Iteration Method (VIM). The usefulness and eectiveness of the approach is demonstrated through the comparison of the obtained results and those achieved by the numerical method. Hence, AGM can be applied to nonlinear problems consisting of signicant nonlinear damping terms and, if necessary, can be easily improved.

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