  We study self-excited oscillations (SEO) in an on-fiber optomechanical
cavity. Synchronization is observed when the optical power that is injected
into the cavity is periodically modulated. A theoretical analysis based on the
Fokker-Planck equation evaluates the expected phase space distribution (PSD) of
the self-oscillating mechanical resonator. A tomography technique is employed
for extracting PSD from the measured reflected optical power. Time-resolved
state tomography measurements are performed to study phase diffusion and phase
locking of the SEO. The detuning region inside which synchronization occurs is
experimentally determined and the results are compared with the theoretical
prediction.
