Exploring small-angle in-plane oscillations of a rigid pendulum suspended from two points: theory and experiment

This study provides an introductory investigation into the oscillatory dynamics of a rigid bar suspended at both ends by two identical, inextensible strings attached to an adjustable horizontal support. Unlike the typical bifilar pendulum—which undergoes torsional motion—this system oscillates within its own plane, combining translational and rotational motion depending on the geometry of the suspension points. A simple theoretical Newtonian model is developed using the small-angle approximation, allowing predictions of the oscillation period and trajectories of the bar’s endpoints. Experimental validation is performed using slow-motion video analysis and tracking software. The results show good agreement between theoretical predictions and experimental observations, highlighting the educational relevance of this system for undergraduate physics students and high school teachers. The setup effectively illustrates constrained rigid body motion and the associated oscillatory and roto-translational behaviours.