  We obtain a master equation for a parametrically driven optomechanical
cavity. We use a more correct dissipation model that accounts for the
modification of the quasienergy spectrum caused by the driving. When the
natural frequency of the mechanical object oscillates periodically around its
mean value, the master equation with the improved dissipation model is
expressed using Floquet operators. We apply the corresponding master equation
to model the laser cooling of the mechanical object. Using an adiabatic
approximation, an analytical expression for the number of excitations of the
mechanical oscillator can be obtained. We find that the number of excitations
can be lower than in the non-time-dependent case. Our results raise the
possibility of achieving lower temperatures for the mechanical object if its
natural frequency can be controlled as a function of time
