This set of exercises guides students through the development of an anharmonic oscillator, then lets them use an ODE solver to plot the motion. It does not describe how to use an ODE solver. Emphasis is on qualitative understanding of the system, although if the instructor chooses it is certainly possible to use real parameters (ρ w a t e r ρ w a t e r, dimensions of boat, etc) to obtain an “engineer’s answer”.

The problem is accessible to first-year students, but it may also be of interest to students in higher-level courses.

There is opportunity to discuss limitations of the model on the final problem. In this problem, if the amplitude is high enough that the boat gets out of the water, the model in the ODE breaks down in interesting and spectacular ways.

The pseudocode, Mathematica notebook, python code, and sample solutions of this Exercise Set assume the use of built-in differential equation solving capabilities. Depending on instructor preference, it may be desirable for students to have experienced the direct application of a finite-difference algorithm to a variety of first-order differential equations before using a computational ‘black box.’