Abstract: Through the Lagrange＇ s equation, the nonlinear vibration equation of a particle non-harmonic oscillator is established; the curves of the restoring force and potential energy varying with coordinates and phase plot are drawn. The exact solution of the period is got by using the first kind of complete elliptic integral. Using the linearization and correction methods, the approximate solutions on period and the displacement of the oscillator are solved, And the curves of the approximate solutions and exact solutions of the period varying with amplitude and the approximate solutions and the numerical solution are drawn by using the Maple 9.5. The approximate solutions have advantages of simplicity, practicality, and higher accuracy, which is of practical value in calculating nonlinear oscillations.

Key words: oscillator, nonlinear vibration, linearization and correction method, period