Quartic oscillator

A bead may move without friction along a horizontal rod, while tied to two symmetric springs, as shown in the figure. The unit length is set to the distance between the rod and the fixed point of each spring, which has proper length L.

Activities

Study analytically the number and stability of the equilibrium points in the following three cases:
- L < 1
- L = 1
- L > 1
Sketch the phase-space in each case.
Use the simulation to check your answers and drawings.

This is an English translation of the Basque original for a course on mechanics, oscillations and waves.
It requires Java 1.5 or newer and was created by Juan M. Aguirregabiria with Easy Java Simulations (Ejs) by Francisco Esquembre.
One may also use Dynamics I thank Wolfgang Christian and Francisco Esquembre for their help. Solver to explore this problem: see this simulation.