Synchronization is the process where two or more systems interact with each other and come to move together. Biology abounds with examples of synchronization: cells in the heart beat together, audiences often applaud together, fireflies in South-East Asia flash in synchrony.
As one metronome's pendulum bob moves to the right, this pushes the base to the left (because of momentum conservation). The base moving to the left then pushes the other metronome's pendulum bob to the right, i.e. in the same direction as the first pendulum. Thus the slightly faster pendulum gives a kick (through the base) to the slower metronome causing the slower pendulum to speed up.
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Some modern buildings in Japan are built using the same conception for prevention of damages during earthquakes. They use a box with water in the top of the buildings that oscillates neutralizing the horizontal movement. Simple, but an efficient idea.
Yes, you have correctly told
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