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.