  We present an experimental study of dynamical back-action cooling of the
fundamental vibrational mode of a thin semitransparent membrane placed within a
high-finesse optical cavity. We study how the radiation pressure interaction
modifies the mechanical response of the vibrational mode, and the experimental
results are in agreement with a Langevin equation description of the coupled
dynamics. The experiments are carried out in the resolved sideband regime, and
we have observed cooling by a factor 350 We have also observed the mechanical
frequency shift associated with the quadratic term in the expansion of the
cavity mode frequency versus the effective membrane position, which is
typically negligible in other cavity optomechanical devices.
