Harmonic and Anharmonic Oscillations of a Boat

Developed by E. Ayars

Easy JavaScript Simulation by Fremont Teng and Loo Kang Wee

Simple Harmonic Oscillation (SHO) is everyone’s favorite type of periodic motion. It’s simple, easy to understand, and has a known solution. But SHO is not the only kind of periodic motion. In this set of exercises we’ll investigate an anharmonic oscillator. We’ll explore characteristics of its motion, and try to get an understanding of the circumstances under which the motion can be approximated as simple harmonic.

Subject Area | Mechanics
Levels | First Year and Beyond the First Year
Available Implementations | Python and Mathematica Easy JavaScript Simulation
Learning Objectives | Students who complete these exercises will be able to use an ODE solver to develop a qualitative understanding of the behavior of an anharmonic oscillator. Most students gain a good understanding of the behavior of harmonic oscillators in their introductory classes, but not all oscillators are harmonic. Here we investigate an idealized boat hull which exhibits asymmetric oscillation: the restoring force is stronger for displacements in one direction than in the other. This results, for large oscillations, in a visibly non-sinusoidal oscillation. For small oscillations, the motion is approximately simple harmonic again.
Time to Complete | 120 min