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

## TL;DR

This paper applies He's frequency-amplitude formulation to accurately analyze nonlinear oscillations of a point charge in a charged ring's electric field, effective for both small and large amplitudes without linearization.

## Contribution

It introduces a specific application of He's method with optimized points, improving accuracy over previous approaches for nonlinear oscillations of a point charge.

## Key findings

- Method achieves high accuracy compared to exact solutions.
- Effective for both small and large amplitude oscillations.
- Outperforms previous methods, especially at large amplitudes.

## Abstract

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.