Molecule 4

This simulation shows 4 masses connected by springs and free to move in 2 dimensions.

You can change parameters in the simulation such as gravity, mass, spring stiffness, and friction (damping). You can drag any mass with your mouse to change the starting position.

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Click the buttons below for various combinations of parameter settings. Can you find all the stable configurations?
1 stable configuration, energy: 4.63
2 stable configurations, energies: 3.55, 3.98
1 stable configuration, energy: 0.48
Very elastic bouncing with no gravity and no damping.
Less elastic bouncing with weak gravity and no damping.
Long red springs, no damping, weak gravity.
With a high amount of damping and no gravity the atoms settle down quickly into various configurations. Notice that two of the springs are red and the rest green. You can set the length or stiffness of the red springs separately from the green springs. By doing so the molecule becomes asymmetric.

The symmetric molecule (all springs are same length and stiffness) is only stable in the square configuration. (Actually it is possible to get to the configuration with the red atom in the center, but it is very unstable and hard to get to).

If you click the button labelled "red spring length 2.5" this will set the red springs to be shorter than the green springs. This makes the molecule asymmetric. Now there are are 2 stable configurations each with a different energy level.

Click the button labelled "red spring length 2" and the red springs are now very much shorter than the green springs. This causes one of the stable configurations to disappear and there is again only 1 stable configurations.

In the study of dynamical systems, this is known as a bifurcation which means that slowly changing a parameter of the system (the spring stiffness here) causes the number of stable states of the system to change.

The energy is calculated as the sum of the kinetic energy (of motion) and the potential energy stored in springs that are stretched from their resting length (gravity also is a source of potential energy).

This web page was first published September 2001.

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