  We present a ground state cooling scheme for a nanomechanical resonator
linearly coupled with a LC oscillator. The linear coupling, when periodically
modulated at red detuning, up-converts the low-frequency nanomechanical mode to
the high-frequency LC oscillator mode and generates backaction force that can
cool the resonator to its ground state in the resolved-sideband regime. We also
study the effect of the quantum backaction noise on the cooling due to the
counter rotating term in the linear coupling. The scheme can be compared with
laser cooling for the atomic systems and can be realized in superconducting
circuits.
