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We consider a single-electron transistor (SET) whose central island is ananomechanical oscillator. The gate capacitance of the SET depends on themechanical displacement, thus, the vibrations of the island vibrations maystrongly influence the current-voltage characteristics, current noise, andhigher cumulants of the current. Harmonic oscillations of the island andoscillations with random amplitude (e.g., due to the thermal activation) changethe transport characteristics in a different way. The noise spectrum has a peakat the frequency of the island oscillations; when the island oscillatesharmonically, the peak reduces to a $\delta$-peak. We show that knowledge ofthe SET transport properties helps to determine in what way the islandoscillates, to estimate the amplitude, and the frequency of the oscillations

Charge transport through a single-electron transistor with a mechanically oscillating island