# Sensing with the harmonic oscillator

## TL;DR

This paper reviews how harmonic oscillators can be used as sensitive force or acceleration sensors, deriving analytical sensitivity expressions considering various noise sources and frequency jitters, and discusses potential sensitivity improvements and applications.

## Contribution

It provides a comprehensive analytical framework for evaluating and enhancing the sensitivity of harmonic oscillator sensors under different noise conditions and frequency fluctuations.

## Key findings

- Derived analytical sensitivity expressions for harmonic oscillator sensors.
- Identified conditions for sensitivity improvements beyond standard limits.
- Discussed practical applications and examples of oscillator-based sensing.

## Abstract

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.