  Using amplitude equations, we show that groups of identical nano-mechanical
resonators, interacting with a common mode of a cavity microwave field,
synchronize to form a single mechanical mode which couples to the cavity with a
strength dependent on the square sum of the individual mechanical-microwave
couplings. Classically this system is dominated by periodic behaviour which,
when analyzed using amplitude equations, can be shown to exhibit
multi-stability. In contrast groups of sufficiently dissimilar nano-mechanical
oscillators may lose synchronization and oscillate out of phase at
significantly higher amplitudes. Further the method by which synchronization is
lost resembles that for large amplitude forcing which is not of the Kuramoto
form.
