  Nanomechanical resonators are used as high performance detectors in a variety
of applications such as mass spectrometry and atomic force microscopy. Initial
emphasis in nanomechanical resonant sensor research was on increasing the
sensitivity to the level of a single molecule, atom and beyond. On the other
hand, there are applications where the speed of detection is crucial, prompting
recent works that emphasize sensing schemes with improved time resolution. We
first develop a general modeling framework encompassing all resonator tracking
schemes currently in use, by extending recent previous work. We then explore
the fundamental trade-offs between accuracy and speed in three resonant sensor
architectures, namely the feedback-free open-loop approach, positive-feedback
based self-sustaining oscillator, and negative-feedback based frequency-locked
loop scheme. We comparatively analyze them in a unified manner, clarify some
misconceptions that seem to exist in the literature, and unravel their speed
versus accuracy characteristics.
