  We study a dynamic mechanism to passively suppress the thermal noise of a
micromechanical resonator through an intrinsic self-feedback that is genuinely
non-Markovian. We use two coupled resonators, one as the target resonator and
the other as an ancillary resonator, to illustrate the mechanism and its noise
reduction effect. The intrinsic feedback is realized through the dynamics of
coupling between the two resonators: the motions of the target resonator and
the ancillary resonator mutually influence each other in a cyclic fashion.
Specifically, the states that the target resonator has attained earlier will
affect the state it attains later due to the presence of the ancillary
resonator. We show that the feedback mechanism will bring forth the effect of
noise suppression in the spectrum of displacement, but not in the spectrum of
momentum.
