How do metronomes synchronize with the Kuramoto mode?
In: 3
The full explanation is complicated, but there’s an intuitive approach.
Note, it’s important that the metronomes are “coupled”, which means that they have some influence on each other.
The synchronisation happens because of this influence. When metronomes are in phase, their energies add up, and they sort of “help eachother” by pushing and pulling in the same way. A bit like pushing on a swing, where if you’re pushing in phase with the swing, you’ll go higher.
Metronomes that are out of phase with each other will instead knock each other and either change or dampen their oscillations.
The other important effect is the idea of stability versus instability. Something that’s stable will tend to go back to where it was when pushed, like a ball at the bottom of a bowl. If you kick the ball, it will roll back. Something unstable does the opposite, if you kick a ball at the top of a hill, it will roll away.
This is the case with coupled metronomes too. Metronomes that are “behind” will tend to accelerate, and metronomes that are “ahead” will tend to slow down.
With just two coupled metronomes, it’s quite easy to see how this will play out, the “late” one will tick faster than the “early” one until they’re synced.
With more metronomes, it’s a bit more difficult to see how they’ll sync up, as all the metronomes will start out ahead of some metronomes and behind others. But they won’t be absolutely perfectly spread out, and whatever *tiny* little bit of synchronisation will slightly pull the metronomes together, getting just a little bit more synchronised with each tick, and that little seed of synchronisation will grow until they’re all in perfect lockstep.
Latest Answers