  We study an optomechanical system consisting of an optical cavity and movable
mirror coupled through dispersive linear optomechanical coupling (LOC) and
quadratic optomechanical coupling(QOC). We work in the resolved side band limit
with a high quality factor mechanical oscillator in a strong coupling regime.
We show that the presence of QOC in the conventional optomechanical system
(with LOC alone) modifies the mechanical oscillator's frequency and reduces the
back-action effects on mechanical oscillator. As a result of this the
fluctuations in mechanical oscillator can be suppressed below standard quantum
limit thereby squeeze the mechanical motion of resonator. We also show that
either of the quadratures can be squeezed depending on the sign of the QOC.
With detailed numerical calculations and analytical approximation we show that
in such systems, the 3 dB limit can be beaten.
