Measuring the frequency of a pendulum

Published

November 13, 2023

Author(s)

Jon R. Pratt, Stephan Schlamminger, Charles Condos, Jack Manley, Dalziel Wilson

Abstract

We previously reported the use of a chip-scale torsion pendulum as a clock gravimeter, exploiting the parametric coupling of its frequency to the local acceleration of gravity and demonstrating micro-g resolution with a silicon nitride prototype. Here, we illuminate aspects of the gravity clock's operation that enhance precision and resolution. The general problem of determining the frequency of a resonator from the motion recorded by a sensor, such as an optical lever, will be explored. We consider the case of a noise-free detector, focusing on the limiting case where measurement of the motion is confounded only by thermomechanical torques randomly driving the pendulum. Mechanisms to enhance precision, such as large amplitude motion of low loss resonators and scaling laws from averaging, are reviewed in the context of uncertainty analysis. We present data for our device that support precision increasing directly in proportion to the ratio of coherent to random motion amplitudes, and inversely with the root of the overall time of observation.

Proceedings Title

Proceedings of the 38th Annual Meeting of the American Society for Precision Engineering

Conference Dates

November 14-17, 2023

Conference Location

Boston, MA, US

Conference Title

38th Annual Meeting of the American Society for Precision Engineering

Pub Type

Conferences

Keywords

micromechanical cock, gravity, noise

Citation

Pratt, J. , Schlamminger, S. , Condos, C. , Manley, J. and Wilson, D. (2023), Measuring the frequency of a pendulum, Proceedings of the 38th Annual Meeting of the American Society for Precision Engineering, Boston, MA, US (Accessed October 8, 2025)