One of the main milestones in the study of opto-mechanical system is to increase the sensitivity of weak forces measurement up to the standard quantum limit. We have studied the detection of weak force under a bistable condition in red detuned regime. In this case, dynamics of the system behaves asymptotically similar to stationary state and applying external force affects phase and fluctuation of the cavity field. Using the signal to noise ratio, we have found the sensitivity of the system to external force. The system show the maximum sensitivity in the region where bistability approaches zero. We also studied the destructive effects of thermal noise on the sensitivity. Our approach is based on the covariance matrix formalism which can be solved by first Lyapunov theorem.