A mass-spring-damper model of a bouncing ball

Mark Nagurka, Shuguang Huang

Research output: Contribution to journalArticlepeer-review

41 Scopus citations


The mechanical properties of a vertically dropped ball, represented by an equivalent mass-springdumper model, are shown to be related to impact parameters. In particular, the paper develops relationships connecting the mass, stiffness and damping of a linear ball model to the coefficient of restitution and the contact time of the ball with the surface during one bounce. The paper also shows that the ball model parameters are functions of quantities readily determined in an experiment: (i) the height from which the ball is dropped from rest, (ii) the number of bounces, and (iii) the time elapsing between dropping the ball and the ball coming to rest. For a ball with significant bounce, approximate expressions are derived for the model parameters as well as for the natural frequency and damping ratio. Results from numerical and experimental studies of a bouncing ping-pong ball are presented.

Original languageEnglish
Pages (from-to)393-401
Number of pages9
JournalInternational Journal of Engineering Education
Issue number2
StatePublished - 20 Apr 2006
Externally publishedYes


  • Coefficient of restitution
  • Dynamics
  • Mass-spring damper model
  • Mechanics

ASJC Scopus subject areas

  • Education
  • General Engineering


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