<![CDATA[The transient response analysis of electrical circuits is fundamental in electrical engineering because it provides insights into the dynamic behavior of circuit components during switching and energy transfer processes. Among various analytical techniques, the Laplace Transform offers an efficient approach for converting time-domain differential equations into algebraic equations in the complex-frequency domain, thereby simplifying the analysis of second-order systems. This study aims to analyze the transient response of a series resistor–inductor–capacitor (RLC) circuit using the Laplace Transform and to validate the analytical model through MATLAB simulation. A quantitative analytical approach combined with numerical simulation was employed. The mathematical model of the circuit was derived from Kirchhoff’s Voltage Law, transformed into the Laplace domain to obtain the transfer function, and evaluated under a 12-V step input. The resistance parameter was varied from 10 Ω to 80 Ω while the inductance and capacitance were maintained constant to investigate underdamped, critically damped, and overdamped responses. The transient characteristics, including rise time, peak time, maximum overshoot, settling time, and steady-state value, were compared between the analytical solution and the simulation results. The results showed that increasing the resistance significantly reduced oscillation and overshoot while improving system stability. The circuit exhibited the fastest non-oscillatory response when the resistance approached the critical resistance, whereas larger resistance values produced slower overdamped responses. Furthermore, the analytical results agreed closely with the MATLAB simulations, confirming the validity of the developed mathematical model. These findings demonstrate that the integration of the Laplace Transform and numerical simulation provides an effective framework for analyzing second-order electrical systems and serves as a practical learning approach for applied mathematics and electrical engineering education.]]>
