Spectral properties of microcantilevers in viscous fluid.

We explore analytically, numerically, and experimentally the spectral properties of the flexural vibrations of micron scale cantilevers in a viscous fluid that are driven externally or by Brownian motion. Although the physical origins of driven and thermal cantilever dynamics are quite different, we show that in each case the dynamics can be calculated deterministically using an impulse or step force, respectively. The stochastic dynamics of the cantilever are related to the removal of a step force by the fluctuation-dissipation theorem to yield the autocorrelation and noise spectral density of equilibrium fluctuations. The dynamics of a cantilever driven externally is related to an impulse in force by transfer function theory. Using this approach, we explore the differences between the driven and thermal spectra of microcantilevers. We find that higher order cantilever modes and the spatial distribution of the applied load for the external drive can be critical to the relationship between the thermal and driven spectra.