Investigation of Mechanical Resonance in a Damped Pendulum Using a Low-Cost, Classroom-Friendly Setup

Abstract

This report presents an investigation into the oscillatory behaviour of a simple pendulum under varying damping conditions and external driving forces, employing a low-cost, easy-to-operate, and visually accessible experimental setup designed for high school classroom demonstrations. The experiment explored both the transient response of free oscillations and the steady-state response under forced oscillations. Free oscillation trials were conducted in air, water, alcohol, and glycerol, representing negligible, light, moderate, and heavy damping regimes respectively. Damping e!ects were quantified by analysing amplitude decay, with characteristic exponential decay observed in light damping and rapid suppression of motion in heavy damping. Forced oscillations were induced through periodic driving, revealing distinct resonance behaviour under light and moderate damping, with resonance peaks shifting lower and broadening as damping increased. The amplitude response curves demonstrated qualitative agreement with the theoretical model of damped driven harmonic oscillators, showcasing key features such as amplitude suppression, phase lag development, and resonance peak broadening. This accessible and low-cost setup e!ectively illustrates fundamental oscillation phenomena, making it a suitable tool for classroom engagement and conceptual reinforcement of damping and resonance principles, with potential extensions to discussions on practical engineering applications such as shock absorption by tuned mass damper and structural resonance control.