  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.
