  We consider a model of a quantum-mechanical resonator capacitively coupled to
a single electron transistor (SET). The tunnel current in the SET is modulated
by the vibrations of the resonator, and thus the system operates as a
displacement detector. We analyze the effect of the back-action noise of charge
fluctuations in the SET onto the dynamics of the resonator and evaluate the
displacement sensitivity of the system. The relation between the "classical"
and "quantum" parts of the SET charge noise and their effect on the measured
system are also discussed.
