By coupling the Lindstedt-Poincare perturbation technique with a rational approximation, we propose a method for summing up the perturbation solutions of the nonlinear oscillation of a conservative single-degree-of-freedom system. The equation of motion contains a parameter, This method can represent the singularities of the period at certain values of the oscillation amplitude and extend the range of validity of the perturbation solution. For constructing the summation, all is needed are the coefficients of the pertubation expansion of the periodic solution. Approximate formulas for the period and the corresponding periodic solution of the nonlinear oscillation are established. Two examples are used to illustrate the effectiveness of the method. [References: 6]
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