The double potential well system is an important basic component of studies of non-linear systems. It is easy to build, simulate, and analyse. It has some intriguing behaviours. It is closely allied to the impacting systems which are of great engineering importance. It may be used as a basic model for many other piecewise linear systems, which are used to model chaotic behaviour in real diodes and transistors used in combination with inductors in chaotic electronic circuits. It also provides a most excellent tool for teaching purposes.