Summary When students have made some progress in studying ordinary differential equations (ODEs) during a semester, small groups are given a soccer ball and asked to determine the simplest model describing one bounce of the ball from shoulder height. To start with, they play with the ball. However, after a few weeks, they begin to ask penetrating questions and they are led to a simple model that has a non-trivial twist to the solution.

Abstract A nonrelativistic model for the classical electrodynamic equations of motion for a radiating particle is investigated. This model is suitable for discussion in a beginning differential equations course and beginning physics course on particle dynamics. It is of interest as it is linear of third order and the third derivative acts as a damping term. Boundedness of the solution becomes of critical importance and conditions are determined for bounded solutions in the unforced and simple sinusoidal forcing cases. The sensitivity of numerical solutions is discussed and further investigations suitable for undergraduate research projects or small student group investigations are suggested.