Motion on cycloid paths: a project

This article reports a high school laboratory project whose theme is the motion of a small ball on cycloidal tracks. Models were built both of a brachistochrone and of a Huygens pendulum clock whose bob is constrained to move on a cycloidal path. Photogates and a data acquisition system were employed in order to investigate experimentally the isochronous property of such a pendulum, as well as the amplitude independence of oscillation periods on the brachistochrone. It was also shown that the times of descent between two points at different heights were always shorter for the brachistochrone than for a variable straight inclined plane. Two appendices provide the theoretical background, accessible to high school students.