  We analyze the response of a nanomechanical resonator to an external drive
when it is also coupled to a single-electron transistor (SET). The interaction
between the SET electrons and the mechanical resonator depends on the amplitude
of the mechanical motion leading to a strongly non-linear response to the drive
which is similar to that of a Duffing oscillator. We show that the average
dynamics of the resonator is well-described by a simple effective model which
incorporates damping and frequency renormalization terms which are amplitude
dependent. We also find that for a certain range of parameters the system
displays interesting bistable dynamics in which noise arising from charge
fluctuations causes the resonator to switch slowly between different dynamical
states.
