We study analytically the synchronization phenomena in a set of globally co
upled oscillators under external periodic driving, with emphasis on the eff
ects of small inertia. We examine in detail both the integer and fractional
mode locking present in the system with inertia, and derive the self-consi
stency equation for the order parameter, which reveals variation of the mag
nitude of the order parameter according to the external periodic driving. I
n particular, it is found that the inertia induces discontinuous transition
s between the coherent and incoherent states. [S1063-651X(99)03701-0].