Computational experiments on the study of electrical oscillations

Abstract

This paper explores the potential of computer modeling methods for studying electrical oscillations in a general physics course. The aim of the study is to develop and implement a system of computational experiments designed to investigate dynamic processes in oscillatory circuits and alternating current circuits, as well as to visualize their fundamental physical characteristics. The proposed approach is implemented using Mathcad 15, which provides numerical solutions to differential equations and graphical representations of the obtained results. Free and forced oscillations are examined, with particular attention to the time-dependent behavior of electric charge, current, and voltage under different circuit operating conditions. Based on mathematical models, time-domain plots and phase portraits are constructed to illustrate the dynamic behavior of the systems and the relationships between their physical parameters. Special emphasis is placed on the analysis of harmonic and non-harmonic periodic oscillatory regimes and the physical interpretation of the corresponding mathematical relationships. The proposed computational experiments complement conventional theoretical and laboratory methods by providing opportunities to visualize physical processes and compare analytical and numerical results. The integration of this approach into physics education is intended to support the development of mathematical modeling skills, graphical data analysis, and the interpretation of computational results. Furthermore, it promotes interdisciplinary connections among physics, mathematics, and computer science, contributing to a more integrated understanding of oscillatory phenomena and their mathematical descriptions.