Sensing with the harmonic oscillator

A system obeying the harmonic oscillator equation of motion can be used as a force or proper acceleration sensor. In this short review we derive analytical expressions for the sensitivity of such sensors in a range of different situations, considering noise of thermal and measurement origins and a formalism for dealing with oscillators whose natural frequency $\omega_0$ jitters. A special case where the sensitivity can be improved beyond the standard expressions and some applications with examples are also discussed.