The mage has five metronomes moving at the same speed, but not synchronized because he started them at different times. Then he places them on a rolling surface. Within a few seconds, they sync up. How? redditor Rangourthaman_ offers an explanation, which you can read by clicking on “more…”
First let’s see what forces there are on a lone metronome:
As the arm swings, it exerts an equal force pushing the casing to the opposite side. It does this with every swing so the metronome itself is constantly trying to go from left to right. Comparable to doing this
So if the metronome is placed on a plank and two cans it will exert force on the plank and move it from left to right.
If we add another metronome, it too,will exert its force on the plank. If it is in sync with the other metronome (Both going left & right at the some time) the force it is exerting on the plank (and thus; the other metronome) will match up as well. (comparable to this)
If the other metronome is in sync but going right when the other is going left they will cancel each other out and reduce the net force on the plank to zero.
When the two are not in sync there can be two possible situations:
One: The two arms are moving in the same direction
Two: The arms are moving in opposite directions.
So what basicaly happens is whenever the arms are not moving in the same direction they are reducing the net energy on the plank to zero thus slowing the plank down. (Because it has friction from the cans.)
When they are moving in the same direction both their energy is transferred to the plank in full, thus giving it more speed and momentum. This momentum is transferred to the first arm that starts to swing back again, giving it the bulk of the energy in the plank and slowing the arm down in the processs. This makes the gap in time between their sync smaller. It does this with every tick, eventually syncing the two up.
Add more metronomes and the same things happens, exept with more indivdual forces, making the proces go smoother.
TLDR: They are forced to the path of least resistance.