Mechanical apparatus for the fold catastrophe demonstration

We present and discuss a non-expensive mechanical experiment which is very suitable for a classroom demonstration of the fold catastrophe behaviour. The apparatus consists of a bar attached to a pulley, to which a hanging body is connected by means of a thread wrapped around its rim. The system may perform stable oscillations or, else, the body may continuously fall down, while the pulley executes a sequence of 360° rotations. This behaviour is analysed in connection with the shape of the potential, which is a good example of a fold catastrophe potential. For the system to perform stable oscillations, that shape reminds a clothes washboard, with local maxima and minima, a potential well known in superconducting quantum computing. We provide some hints for the instructor to explore the device in lab classes. MF and RN are grateful to the Portuguese Physical Society and to the Royal Spanish Physical Society for the invitations to deliver talks during their national meetings on 'Catastrophic potentials'. These talks were motivational to write the paper.