  In the usual optomechanical systems, the stability of the systems severely
limits those researches of the macroscopic quantum effects. We study an usual
cavity optomechanical system where the frequency of the optical mode is shaken
periodically. We find that, when the optical shaking frequency is large enough,
the shake of the optical mode can stabilize the system. That means we can study
the macroscopic quantum effects of the mechanical resonator even in the strong
coupling region where the standard optomechanical systems are always unstable.
As examples, we study the ground-state cooling of the mechanical resonator and
the entanglement between the optical and mechanical modes in the conventional
unstable region, and the results indicate that the final mean phonon number and
entanglement not only can be achieved but also can be modulated by the optical
shaking parameters. Our proposal provides a method to study the macroscopic
quantum effects even in conventional unstable region.
