Ordered and chaotic motion of a forced spherical pendulum

It is known theoretically that a forced spherical pendulum can develop complex and sometimes chaotic patterns of motion. An effective demonstration apparatus has been constructed on this principle. A procedure is described for using the apparatus to contrast chaotic motion with an ordered, but not trivially obvious, pattern of motion. More detailed observations of the pendulum show that it illustrates much of the complexity typical of systems undergoing transition to chaos. A satisfactory comparison of its behaviour may be made with the theory, despite unavoidable differences between the two and the essentially qualitative nature of the apparatus.