Developed by Eric Ayars  Published August 1, 2016
DOI: 10.1119/PICUP.Exercise.anharmonic
Subject Area  Mechanics 

Levels  First Year and Beyond the First Year 
Available Implementations  Python, IPython/Jupyter Notebook, Mathematica, and Easy Java Simulations 
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 nonsinusoidal oscillation. For small oscillations, the motion is approximately simple harmonic again.

Time to Complete  120 min 
These exercises are not tied to a specific programming language. Example implementations are provided under the Code tab, but the Exercises can be implemented in whatever platform you wish to use (e.g., Excel, Python, MATLAB, etc.).
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Credits and Licensing
Eric Ayars, "Harmonic and Anharmonic Oscillations of a Boat," Published in the PICUP Collection, August 2016, https://doi.org/10.1119/PICUP.Exercise.anharmonic.
DOI: 10.1119/PICUP.Exercise.anharmonic
The instructor materials are ©2016 Eric Ayars.
The exercises are released under a Creative Commons AttributionNonCommercialShareAlike 4.0 license