Abstract
Mathematical and physical aspects in the analysis of pendulum motion in the presence of quadratic and linear damping are presented. New results are obtained from the analysis which are of research and educational interest. Closed-form expressions for the velocity vs large angle of swing are derived in the case of quadratic damping for both forward and backward swings. In the case of linear damping, there is no closed-form expression for the velocity vs large angle of swing, but an implicit relationship between the velocity and small angle of swing is derived and discussed. The derived formulas are useful for the determination of the amplitudes of the pendulum swings corresponding to given initial velocities and for the evaluation of the dissipated energy at any stage of the pendulum motion. Instructive project-based activities are suggested, which are suitable for collaborative learning and undergraduate student research.
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