Nonlinearly-damped oscillator simulation

Simulates a driven harmonic oscillator with nonlinear damping and compares results to a resonance model with amplitude-dependent width.

The driven harmonic oscillator with linear damping is a model for a multitude of phenomena. But the simplest mechanical oscillators are damped by air drag quite nonlinear in velocity. This script performs a numerical study of a harmonic oscillator subject to a harmonic external force and to a drag force quadratic in speed approximating air drag. The resonance height and shape compare well with a linear model adjusted to have an amplitude-dependent width. The script may be readily modified to study other nonlinear resonance phenomena and may interest physics and engineering students and instructors encountering nonlinear air drag in laboratory experiments or analytic explorations using perturbation theory in intermediate-level mechanics. Try this suggestions are included for further exploration.