Abstract:

The Newtonharmonic balance method was used to construct analytical approximate periods and periodic solutions to the relativistic harmonic oscillator. Introducing a new variable and rewriting the control equation in terms of the new variable, we applied the Newton-harmonic balance method to solving the resulted equation. The method yields rapid convergence with respect to exact solution, and the analytical approximations obtained are valid for the whole range of initial oscillation amplitudes. The approximate periods and periodic solutions are excellently agreed with the exact ones.

Key words: relativistic harmonic oscillators, Newtonharmonic balance method, analytical approximation