What is the oscillation amplitude of a vibrating cantilever?

Abstract

Resonant amplification of vibrational amplitude underpins the application of nanomechanical sensors. For cantilever sensors, this amplification is widely reported to be equal to the sensor's quality factor, which strongly underestimates its true value. Here, we present a simple analytical formula for this amplification factor, valid for three-dimensional resonators of arbitrary shape, that will find utility in practice.