Addendum: Modeling the amplitude and energy decay of a weakly damped harmonic oscillator using the energy dissipation rate and a simple trick (2025 Eur. J. Phys. 46(1) 015004)

2024/11/23 by Karlo Lelas, Lelas, Karlo, Pezer, Robert
Computer Science · #Nonlinear Dynamics and Pattern Formation

paper · pdf · doi:10.48550/arxiv.2411.15588

Abstract

We show how to adapt the approach introduced for viscous damping in [1] to derive the approximate amplitude decay in the case of damping by a force of constant magnitude (sliding friction) and in the case of damping by a force proportional to the square of velocity (air resistance). We obtain two first-order differential equations from which we obtain the approximate time-dependent amplitudes corresponding to the considered damping forces. Our approach is suitable for first-year undergraduates, as it relies on the physical concepts and mathematical techniques they are familiar with.

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