A techie explanation...
In a system of linear oscillators like this one, the motion can be described by the sum of a set of "modes", each of which oscillates at a single frequency. At the beginning, the oscillators are effectively uncoupled (they'll be weakly coupled through the table, but this is too heavy to really make a difference). There are therefore 5 modes, each describing a single metronome oscillating at its own frequency. When the metronomes are put on a common board, which is capable of moving from side to side, the modes will become coupled and will describe the motion of all the metronomes in some way. Key is that the different modes lose energy at different rates due to non-linear effects (damping). The motion that you see at the end, with all the metronomes in sych is a single mode and it happens to be the one that loses energy the slowest. All the other modes therefore die away leaving only that motion being observed.
(, Wed 7 May 2008, 16:54, Share, Reply)