A model describing optomechanical dynamics via radiation-pressure coupling with a driven optical cavity is investigated by a linearized quantum Langevin equation. The spectrum of the oscillator presents normal mode splitting with the increase of the input laser power in strong coupling regime and our results are in good agreement with the experimental results. The effective mechanical damping and the resonance frequency shift are derived. The redshifted sideband leads to the cooling of the mechanical oscillator, and the blueshifted motional sideband results in amplification. Furthermore, an approximate mechanism is introduced to analyze the 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 influences the cooling of the mirror is considered. Meanwhile, we give three key factors influencing the cooling of mechanical oscillator, these being initial bath temperature, input laser power and mechanical quality factor.