  We propose a spectrometric method to detect a classical weak force acting
upon the moving end mirror in a cavity optomechanical system. The force changes
the equilibrium position of the end mirror, and thus the resonance frequency of
the cavity field depends on the force to be detected. As a result, the
magnitude of the force can be inferred by analyzing the single-photon emission
and scattering spectra of the optomechanical cavity. Since the emission and
scattering processes are much faster than the characteristic mechanical
dissipation, the influence of the mechanical thermal noise is negligible in
this spectrometric detection scheme. We also extent this spectrometric method
to detect a monochromatic oscillating force by utilizing an optomechanical
coupling modulated at the same frequency as the force.
