  The cooling performance of an optomechanical system comprising both
dispersive and dissipative coupling is studied. We present a scheme to cool a
mechanical resonator to its ground state in finite time by employing a chirped
pulse. When the cavity damping strength increases, the phonon occupation of the
resonator will decrease. Moreover, the cooling behaviors of this dispersively
and dissipatively coupled system with different incident pulses, different
system coupling strengths are explored. Our scheme is feasible to cool the
resonator in a wide parameter region.
