In this paper, a new method for solving the non-linear dynamic systems by numerical integral method is established. This exact solution is calculated by means of the Duhamel integral. The system equations are satisfied continuously and not discretely as done traditionally. The essential difference of the present method from other works is that the performance of dynamics systems can be traced continuously. Comparisons between the proposed method with traditional techniques are presented. Examples investigated include the large amplitude nonlinear vibration of a simple pendulum of conservation systems, the period of vibration and chaos in the forced vibration of the Van der Pol oscillator of a non-conservation system. The results obtained indicate that the accuracy of the proposed method supersede that of the traditional techniques.

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