  We consider a single-electron transistor (SET) whose central island is a
nanomechanical oscillator. The gate capacitance of the SET depends on the
mechanical displacement, thus, the vibrations of the island vibrations may
strongly influence the current-voltage characteristics, current noise, and
higher cumulants of the current. Harmonic oscillations of the island and
oscillations with random amplitude (e.g., due to the thermal activation) change
the transport characteristics in a different way. The noise spectrum has a peak
at the frequency of the island oscillations; when the island oscillates
harmonically, the peak reduces to a $\delta$-peak. We show that knowledge of
the SET transport properties helps to determine in what way the island
oscillates, to estimate the amplitude, and the frequency of the oscillations.
