A steel ball bounces in synchronism with a vertically oscillating piston. The piston surface is a hardened steel disk on which the ball bounces; two−dimensional horizontal focusing is provided by the concavity of the surface. The period of oscillation can be varied over a 3:1 range with the amplitude kept constant. As the period is increased, the ball bounces higher. As the period is decreased, the ball bounces lower, contrary to the intuition of most observers. The model illustrates the important properties of synchrotron accelerators.