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The homotopy perturbation method with an auxiliary term is applied to obtain an approximate analytical solution for the tangent nonlinear packaging system. To further raise the accuracy of the solution, this work has expanded the possibility of the energy method for the homotopy perturbation method with an auxiliary term. And then, the amplitude and frequency of the tangent nonlinear packaging system can be calculated. The results show that the solution is in good consistent with the numerical solution solved by the Runge–Kutta method. It can be concluded that the proposed method is suitable for the optimal design of a tangent nonlinear packaging system.