  The mirror relative motion of a suspended Fabry-Perot cavity is studied in
the frequency range 3-10 Hz. The experimental measurements presented in this
paper, have been performed at the Low Frequency Facility, a high finesse
optical cavity 1 cm long suspended to a mechanical seismic isolation system
identical to that one used in the VIRGO experiment. The measured relative
displacement power spectrum is compatible with a system at thermal equilibrium
within its environmental. In the frequency region above 3 Hz, where seismic
noise contamination is negligible, the measurement distribution is stationary
and Gaussian, as expected for a system at thermal equilibrium. Through a simple
mechanical model it is shown that: applying the fluctuation dissipation theorem
the measured power spectrum is reproduced below 90 Hz and noise induced by
external sources are below the measurement.
