A mass-spring-damper model of a bouncing ball

The mechanical properties of a vertically dropped ball, represented by an equivalent mass-spring-damper model, are related to the coefficient of restitution and the time of contact of the ball during one bounce with the impacting surface. In addition, it is shown that the coefficient of restitution and contact time of a single bounce are related to the total number of bounces and the total time elapsing between dropping the ball and the ball coming to rest. For a ball with significant bounce, approximate expressions for model parameters, i.e., stiffness and damping or equivalently natural frequency and damping ratio, are developed. Experimentally based results for a bouncing pingpong ball are presented.