Periodic motion of a mass–spring system

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.