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IMA Journal of Applied Mathematics Advance Access published online on October 27, 2009
IMA Journal of Applied Mathematics, doi:10.1093/imamat/hxp032
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© The Author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Periodic motion of a mass–spring system

Michael Shearer{dagger}, Pierre Gremaud and Kristoph Kleiner

Department of Mathematics and Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695, USA

{dagger} Email: shearer{at}ncsu.edu

Received on June 6, 2007; Revision received May 9, 2009. Accepted on May 20, 2009

The equations of planar motion of a mass attached to two anchored massless springs form a symmetric Hamiltonian system. The system has a single dimensionless parameter L, corresponding to the spacing between the anchors. For L > 1, there is a stable equilibrium at which the springs are in tension and lie on a line, but for L < 1, this equilibrium has both springs in compression and is unstable. However, there are then two stable equilibria at which both springs carry no force. Oscillations are studied in both regimes, but more systematically in the tension case, where techniques of bifurcation theory, numerical approximation and numerical simulation are used to explore the rich variety of periodic solutions.

Keywords: mass-spring system; Hamiltonian system; periodic solutions.


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