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myphysicslab – molecule 5

this simulation shows 5 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. if you don't see the simulation try instructions for enabling java.

click the buttons below for various combinations of parameter settings. can you find all the stable configurations?
4 stable configurations, energies: 14.25, 14.25, 14.25, 18.21
4 stable configurations, energies: 11.07, 11.43, 13.12, 13.70
3 stable configurations, energies: 5.62, 5.97, 9.18
very elastic bouncing with no gravity and no damping.
less elastic bouncing with weak gravity and no damping.
with a high amount of damping (eg. damping set to 1.0) the atoms settle down quickly into various configurations. notice that two of the springs are red and the rest green. we 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 & stiffness) has 4 stable configurations that appear different in regards to the positioning of the red vs. green springs. but 3 of these configurations have the same energy. 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).

if you click the button labelled "red spring stiff 3" this will set the red springs to be weaker than the green springs. this makes the molecule asymmetric, or unbalanced. now the same 4 configurations are present, but they are distorted and each has a different energy.

if you click the button labelled "red spring stiff 1" the red springs are now very much weaker than the green springs. this causes one of the stable configurations to disappear and merge into one of the other stable configurations. so now there are only 3 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.
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