Stochastic excitation and delayed oscillation of a micro-oscillator

Stochastic processes in the form of the classical Brownian motion or internal phonon fluctuations may be studied by the use of a microcantilever. We present certain dynamic aspects of the behavior of the noise and the delayed fluctuations exhibited by a microcantilever. In particular, we present an analytic solution describing the transient response of the oscillator and discuss how self-excitation may determine the presence of small delays and, conversely, how delay-induced excitation may provide sensory information. As an application of the analysis, we present dynamic measurement of surface displacement with a preliminary sensitivity of 2 Hz μm in the chosen frequency window, which may effectively be extended to the nanometer regime.