Revisiting the Coulomb-Damped Harmonic Oscillator
Abstract
The force of dry friction is studied extensively in introductory physics but its effect on oscillations is hardly ever mentioned. Instead, to provide a mathematically tractable introduction to damping, virtually all authors adopt a viscous resistive force. While exposure to linear damping is of paramount importance to the student of physics, the omission of Coulomb damping might have a negative impact on the way the students conceive of the subject. In the paper, we propose to approximate the action of Coulomb friction on a harmonic oscillator by a sinusoidal resistive force whose amplitude is the model's only free parameter. We seek the value of this parameter that yields the best fit and obtain a closed-form analytic solution, which is shown to nicely fit the numerical one.
Cite
@article{arxiv.1908.10363,
title = {Revisiting the Coulomb-Damped Harmonic Oscillator},
author = {Joseph A Rizcallah},
journal= {arXiv preprint arXiv:1908.10363},
year = {2019}
}
Comments
9 pages, 5 figures, typos corrected