A detailed analysis of pendular motion is presented. Inertial effects, self-oscillation, and memory, together with non-constant moment of inertia, hysteresis, and negative damping are shown to be required for the comprehensive description of the free pendulum oscillatory regime. The effects of very high initial amplitudes, friction in the roller bearing axle, drag, and pendulum geometry are also analyzed and discussed. A model consisting of a fractional differential equation fits and explains high resolution and long-time experimental data gathered from standard action-camera videos.

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See supplemental material at https://doi.org/10.1119/10.0001660 for (i) a detailed description of the OPA model; (ii) motivations to learn fractional calculus; (iii) a numerical method to solve a fractional differential equation; (iv) an additional bibliography; and (v) additional figures.

Supplementary Material

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