More Coupled Pendulums

The earlier Coupled Pendulums Applet had a large pendulum, coupled to a rectangular array of 119 smaller pendulums. The idea was to simulate the second law of thermodynamics. Although I expected the energy from the large pendulum to be dispersed amoung the smaller ones, this didn't happen. A discussion on sci.physics.research suggested that moving up to 3 dimensions, or introducing more irregularity might get it to do what I expected. Hence I modified the original applet to give the one below. This has a 16×5×8 array of pendulums. The dynamics of the system is explained on the original applet page.

You can choose which pendulums you want to have in the system by checking or unchecking the boxes on the right. Alternatively you can choose what proportion of the boxes you want checked by moving the slider and then pressing the 'Fill' button. The boxes will then be randomly filled. You will need to press the 'Reset' button to start the simulation with the new settings.

And the result is..

You will probably notice that the changes don't make any difference to the original behaviour. The energy of the large pendulum still isn't dispersed amoung the smaller one's. So it doesn't look like this will give the reason for the system not behaving as expected.

One thing that was pointed out in the messages on sci.physics.research was that a similar 'virtual experiment' was done 50 years ago by Fermi, Pasta and Ulam, so it looks like the best idea would be to see what followed on from this. I also intend to look at similar simuilations where I would expect to see dispersal of energy, such as modelling a gas.