We analyze the occurrence of the synchronization phenomenon, in which two or more objects in a system move in unison. We use a purely classical system consisting of N small oscillators exhibiting metronomic behavior coupled to each other through a larger substrate oscillator. We determine the equations of motion of the system and numerically solve them for the position as a function of time to see whether we are able to get the synchronization for N small oscillators. We found that the synchronization occurs after some necessary time intervals, which are referred to as stabilizing time σ and synchronization time τ. By application of scaling laws, we found that τ depends only on the small oscillator’s and substrate’s masses and damping constants. In the analysis, we investigate the conditions which are required to get a nontrivial synchronization for this classical system.
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