Accuracy of Numerical and Analytical Models for Nonlinear Pendulum Motion
DOI:
https://doi.org/10.58445/rars.3071Keywords:
Pendulum motion, Oscillatory systems, Nonlinear dynamicsAbstract
This paper studies the accuracy of various theoretical models of pendulum oscillatory motion by comparing them to experimentally determined data. Pendulums, though often simplified in introductory physics, display nonlinear behavior at large amplitudes, along with significant damping effects. To explore this, equations of motion for the small-angle approximated, drag-free and drag-induced model were solved numerically in Python, and compared to experimental data. Results showed the increasing unreliability of the small-angle approximated and drag-free model with larger amplitudes. At these angles of release, only the drag-induced model sufficiently captures amplitude and period decay, though its accuracy depends strongly on damping coefficient setup.
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