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We study the spectral effect of the fluctuations of the vibration frequency.Such fluctuations play a major role in nanomechanical and other mesoscopicvibrational systems. We find that, for periodically driven systems, theinterplay of the driving and frequency fluctuations results in specificspectral features. We present measurements on a carbon nanotube resonator andshow that our theory allows not only the characterization of the frequencyfluctuations but also the quantification of the decay rate without ring-downmeasurements. The results bear on identifying the decoherence of mesoscopicoscillators and on the general problem of resonance fluorescence and lightscattering by oscillators.

Interplay of driving and frequency noise in the spectra of vibrational systems