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An asymmetrical double torsion pendulum for studying coupled harmonic motion

In this study, a simple asymmetrical double torsion pendulum is built and operated to study coupled harmonic motion. The setup, which consists of two circular inertia members suspended horizontally at different locations on a vertical guitar wire, has a close mechanical similarity to a wall-spring-mass-spring-mass system. The restoring torque of the twisted guitar wire drives the two inertia members to rotate in the horizontal plane. A smartphone and target-tracking software are used to measure the normal frequencies, which are found to reside in two different frequency bands separated by an obvious frequency gap. The described setup has several pedagogical advantages, including easy accessibility, good accuracy, and continuous tunability, and is thus an effective means for engaging students with topics such as mechanical similarity, moment of inertia, torque constant, normal frequency, and target tracking. Teachers can also use the setup as a simple classical analogy to interpret the mechanical shift of the vibrational frequency of a diatomic molecule adsorbed on a sample surface.