ANALYSIS OF NONLINEAR OSCILLATORY DYNAMICS IN A FOUR-CHARGE ELECTROSTATIC SYSTEM

This study investigates the dynamics of non-harmonic oscillations arising in a system of four identically charged small spheres arranged in a regular quadrilateral and connected by silk threads of equal length. In the absence of gravity, the system is initially in electrostatic equilibrium. A disturbance is introduced by burning one of the connecting threads, causing an imbalance that leads to motion driven by Coulomb repulsion among the charges. Despite the internal motion, the center of mass of the system remains stationary due to the symmetry of the forces involved. To analyze the resulting oscillatory behavior, a system of differential equations governing the motion of the charges is formulated. These equations are solved numerically using the improved Euler method. The implementation is carried out using Microsoft Excel and VBA (Visual Basic for Applications), providing an accessible yet effective computational framework. The simulation reveals the nature and approximate period of the resulting non-harmonic oscillations. This work contributes to the broader understanding of charge interactions in constrained systems and serves as a model for exploring similar configurations in electrostatics and nonlinear dynamics