Elastic pendulum

A mass can move along an articulated rod while a spring links it with the articulation. Friction is negligible. The simulation can be used to explore the motion, including the normal modes. It is also possible to draw the Poincaré section dr/dt = 0.
On the right the mass orbit (and/or the Poincaré section) is displayed and one can also get the evolution of the polar variables r(t) and φ(t).

The unit mass is that of the block m.
The unit length is spring's natural length l.
The unit time is (l/g)^1/2.
In these units m = l = g = 1.

Activities

Try different initial conditions and discuss the different kinds of motion.
Selecting Poincaré will draw the points at which the radial velocity dr/dt vanishes. This may help (with or without Orbit) classifying the solutions.
Put the system in its configuration of stable equilibrium and check it does not move from it.
Put the system in each of its normal modes
Enable Graphics and check the normal frequencies.

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. I thank Wolfgang Christian and Francisco Esquembre for their help.