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In this paper we present an experimental setup and an associated mathematicalmodel to study the synchronization of two self sustained strongly coupledmechanical oscillators (metronomes). The effects of a small detuning in theinternal parameters, namely damping and frequency, have been studied. Ourexperimental system is a pair of spring wound mechanical metronomes, coupled byplacing them on a common base, free to move along a horizontal direction. Inour system the mass of the oscillating pendula form a significant fraction ofthe total mass of the system, leading to strong coupling of the oscillators. Wemodified the internal mechanism of the spring-wound "clockwork" slightly, suchthat the natural frequency and the internal damping could be independentlytuned. Stable synchronized and anti-synchronized states were observed as thedifference in the parameters was varied. We designed a photodiode array basednon-contact, non-magnetic position detection system driven by a microcontrollerto record the instantaneous angular displacement of each oscillator and thesmall linear displacement of the base coupling the two. Our results indicatethat such a system can be made to stabilize in both in-phase anti-phasesynchronized state by tuning the parameter mismatch. Results from bothnumerical simulations and experimental observations are in qualitativeagreement and are both reported in the present work.

Effect of parameter mismatch on the synchronization of strongly coupled self sustained oscillators