Waggling pendulums and visualization in mechanics

Peter S. Cumber*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


Students often find mechanics a difficult area to grasp. This article describes an equation of motion for a waggling pendulum. A wide range of pendulum dynamics can be simulated with this model. The equation of motion is embedded in a graphical user interface for its numerical solution in MATLAB. This allows a student's focus to be on the influence of different parameters on the pendulums dynamics. The simulation tool can be used as a dynamics demonstrator in a lecture or as an educational tool driven by the imagination of the student. By way of demonstration, the simulation tool has been applied to different damped pendulums including an inverted pendulum. The model has also been used to simulate resonance and has shown that there is a wide range of behaviours possible depending on the type of forcing applied.

Original languageEnglish
JournalInternational Journal of Mathematical Education in Science and Technology
Early online date15 Dec 2014
Publication statusPublished - 2014


  • animation
  • damped pendulums
  • GUI
  • inverted pendulums
  • mechanics
  • resonance

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematics (miscellaneous)
  • Education


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