MATLAB-Simulation-Based Analysis of Free RLC Oscillations

Abstract

Targeting the LC oscillation commonly taught in high school, this study models a series RLC circuit using university-level circuit theory and ordinary differential equations. We derive the analytical solutions for the underdamped, critically damped and overdamped regimes, compare their time responses and energy dissipation, and visualize charge, current, and total energy via MATLAB. The work offers a quantitative, visual reference to bridge high-school and university instruction, and clarifies two often-confused issues: the opposite trends of the Q factor with resistance in series and parallel RLC circuits, and the condition under which critical damping is the fastest route to equilibrium. The main contributions are: (1) a classroom-oriented set of simulation plots for all three damping regimes; (2) a unified formulation based on the damping ratio and on energy dissipation; (3) simple guidance on how R, L and C affect the damping behavior.