Rocking oscillatory motion and a technique for its measurement

Equations are derived giving the period of rocking oscillatory motion of various bodies when placed on a flat horizontal surface, displaced from equilibrium, and released. The bodies include a sphere and a circular disk with a flat surface, a circular disk with a circular hole, and elliptical disks with circular and elliptical holes. A technique that can be used in an undergraduate mechanics laboratory is described for determining the period of rocking oscillatory motion. The technique consists of measuring the frequency with which electrical continuity is completed when a metallic body instantaneously makes contact with two conducting plates as it undergoes rocking oscillatory motion. The timing is accomplished with digital electronics.