Nonlinear oscillations of a point charge in the electric field of charged ring using a particular He's frequency-amplitude formulation

In this paper, He's frequency-amplitude formulation with some choice of location points that improve accuracy is applied to determine the periodic solution for the nonlinear oscillations of a punctual charge in the electric field of charged ring. The results of the present study are valid for small and large amplitudes of oscillation. The present method can be applied directly to highly nonlinear problems without any discretization, linearization or restrictive assumptions. Finally, compared with the exact solution shows that the result obtained is of high accuracy and we will do a comparative study with previous research done on the same problem, we will see that our approach is much better especially for large amplitude values.