We study the synchronization phenomena in systems of globally coupled oscil
lators, each possessing finite inertia, with particular attention to the no
ise effects. The self-consistency equation for the order parameter as well
as the probability distribution is obtained from the Smoluchowski equation,
and analyzed in the presence of thermal noise. It is found that the hyster
esis present in the system without noise disappears as the thermal noise co
mes into the system. Numerical simulations are also performed to give resul
ts generally consistent with the analytical ones.