How about that Bayes: Bayesian techniques and the simple pendulum

TL;DR

This paper demonstrates how Bayesian techniques can be applied to analyze simple pendulum experiments, providing quantitative guidance for model selection and improving teaching laboratory practices.

Contribution

It introduces a Bayesian workflow for pendulum data analysis, offering a practical approach for model comparison in educational settings.

Findings

Bayesian methods effectively distinguish between small angle approximation and complex models.

Quantitative guidance improves laboratory experiment design.

Bayesian analysis enhances understanding of pendulum dynamics in teaching labs.

Abstract

Physics increasingly uses Bayesian techniques for systematic data analysis and model-to-data comparison. This paper describes how these methods can be implemented to answer questions of relevance to teaching laboratories. It demonstrates the Bayesian approach to statistical modeling and model selection in a step-by-step workflow. The simple pendulum provides a demonstration with the precision commonly seen in the introductory laboratory. This is used to provide realistic, quantitative guidance for model preference between the small angle approximation and more complicated formula. This extends the simple pendulum literature's focus beyond comparing individual idealized assessments of different approximations and provides actionable, data-driven guidance for teaching laboratory design.