Experimental and numerical study of nonsmooth maximum bounce height changes in a bouncing ball system

The bouncing ball system is a simple mechanical collision system that has been extensively studied for several decades. In this study, we investigate the bouncing ball's dynamics both numerically and experimentally. We implement the system using a table tennis ball and paddle vibrated by a shaker. We focus on the relationship between the ball's maximum bounce height in the long time interval and the paddle's vibration frequency, observing several stepwise height changes for frequencies of 25-50 Hz, noting this significant characteristic in both our experiments and numerical simulations. We concentrate on this paddle frequency interval because the phenomenon is easy to handle in numerical simulations. Because the observed phenomenon has a simple order, it can be universal and appear in a large class of collision dynamics. Possibly, some researchers have investigated the bouncing ball system in which the nonsmooth maximum bounce height changes occur. However, they may have failed to notice the changes because the maximal height of the ball was not considered.