A model describing optomechanical dynamics via radiation-pressure coupling with a driven optical cavity was investigated by a linearized quantum Langevin equation under resolved sideband regime. Both the movable mirror and output field present the normal mode splitting with increasing of the input laser power and the results approach the experiment very well. The effective mechanical damping and resonance frequency shift are derived. The redshift sideband leads to cooling of the mechanical oscillator and the blueshift motional sideband results in amplification. Furthermore, an approximation scheme is introduced to analyze cooling of the mechanical oscillator. Since both the normal mode splitting and cooling require working in the resolved sideband regime, whether the normal mode splitting influence cooling of the mirror is considered. Meanwhile, the key factors that dominate the ground state cooling are also discussed.