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

Abstract

In this paper we present an experimental setup and an associated mathematical model to study the synchronization of two self sustained strongly coupled mechanical oscillators (metronomes). The effects of a small detuning in the internal parameters, namely damping and frequency, have been studied. Our experimental system is a pair of spring wound mechanical metronomes, coupled by placing them on a common base, free to move along a horizontal direction. In our system the mass of the oscillating pendula form a significant fraction of the total mass of the system, leading to strong coupling of the oscillators. We modified the internal mechanism of the spring-wound "clockwork" slightly, such that the natural frequency and the internal damping could be independently tuned. Stable synchronized and anti-synchronized states were observed as the difference in the parameters was varied. We designed a photodiode array based non-contact, non-magnetic position detection system driven by a microcontroller to record the instantaneous angular displacement of each oscillator and the small linear displacement of the base coupling the two. Our results indicate that such a system can be made to stabilize in both in-phase anti-phase synchronized state by tuning the parameter mismatch. Results from both numerical simulations and experimental observations are in qualitative agreement and are both reported in the present work.