The kinematics and static equilibria of a Slinky

Peter Cumber*

*Corresponding author for this work

Research output: Contribution to journalComment/debatepeer-review

1 Citation (Scopus)
113 Downloads (Pure)


A Slinky is a loose helical coil spring and is a well-known educational toy. In this paper a model for a Slinky is presented. The Slinky is represented as a sequence of rigid half coils connected by torsional springs. A range of Slinky configurations in static equilibrium are calculated. Where possible the torsion spring model is compared with the much simpler point mass model of a Slinky, and a more sophisticated model that includes axial and shear deformation. The torsional spring model is shown for the most part to produce similar qualitative behaviour as the more complex model. The simplicity of the torsional spring model makes it a candidate for a discrete stair walking dynamic model of a Slinky, The point mass model is straightforward to derive and solve and makes it possible for an undergraduate engineering student in the early part of their degree course to understand. The torsional spring model is a useful tool for showing what can be done in a more advanced mechanics course to model a system that most students would have previous experience of.

Original languageEnglish
Pages (from-to)1065-1083
Number of pages19
JournalInternational Journal of Mathematical Education in Science and Technology
Issue number4
Early online date12 Oct 2022
Publication statusPublished - 20 Apr 2024


  • bifurcation
  • Mechanics
  • numerical optimization
  • Slinky

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Education
  • Applied Mathematics


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