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)

TL;DR

This paper presents a simple method for modeling amplitude and energy decay in weakly damped harmonic oscillators with different damping forces, making it accessible for first-year students.

Contribution

It adapts an existing approach to include damping by sliding friction and air resistance, deriving approximate amplitude decay equations suitable for educational purposes.

Findings

Derived first-order differential equations for amplitude decay.

Applicable to damping by sliding friction and air resistance.

Suitable for teaching first-year undergraduate physics.

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.