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

Shu Karube1, Takuji Kousaka2, Naohiko Inaba3

  • 1Department of Mechanical Engineering, National Institute of Technology, Oita College, Oita 870-0152, Japan.

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Summary

This study reveals stepwise changes in a bouncing ball's maximum height with paddle vibration frequency. These dynamics, observed experimentally and numerically, offer insights into universal collision phenomena.

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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.