Lagrange's method applied to a Slinky

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The Lagrange method is applied to two dynamic models of a Slinky, one based on point masses and linear springs and a second where the Slinky is represented as a sequence of half hoops connected by torsion springs. For the first time, the use of Lagrange's method applied to a Slinky has produced a multi-body dynamic model that can potentially with minor modification reproduce all the interesting behaviour Slinkies are well known for; descending stairs, pseudo levitation, transmission of longitudinal and transverse waves. In this paper, the models are derived and a limited exploration of the two dynamic models’ behaviour is considered. For unforced oscillation, the point mass model and torsion spring model produce a similar amplitude and frequency. When considering forced oscillations, the point mass model has a very different spectrum of natural frequencies than the torsion spring model. The torsion spring model is considered for different forcing conditions.
Original languageEnglish
JournalInternational Journal of Mechanical Engineering Education
Early online date30 Jul 2023
Publication statusE-pub ahead of print - 30 Jul 2023


  • Lagrange's method
  • Mechanics
  • Slinky

ASJC Scopus subject areas

  • Education
  • Mechanical Engineering

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