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

Area of Science:

• Mechanical Engineering
• Nonlinear Dynamics
• Experimental Physics

Background:

• The bouncing ball system is a classic model in mechanical collision studies.
• Previous research has explored its dynamics, but specific phenomena may have been overlooked.
• Understanding complex collision behaviors is crucial for various engineering applications.

Purpose of the Study:

• To investigate the dynamics of a bouncing ball system numerically and experimentally.
• To analyze the relationship between the ball's maximum bounce height and paddle vibration frequency.
• To identify and characterize stepwise changes in bounce height within a specific frequency range.

Main Methods:

• Implementation of a bouncing ball system using a table tennis ball and a vibrated paddle.
• Conducting experiments with varying paddle vibration frequencies (25-50 Hz).
• Performing numerical simulations to complement experimental observations.

Main Results:

• Observed distinct stepwise changes in the maximum bounce height of the ball.
• These changes were consistently found across both experimental and numerical investigations.
• The phenomenon was particularly evident within the 25-50 Hz paddle frequency range.

Conclusions:

• The study highlights a significant, yet potentially overlooked, characteristic of bouncing ball dynamics.
• The observed stepwise height changes are simple, suggesting universality in collision dynamics.
• This finding could prompt re-examination of similar systems where maximal height changes were not considered.