A simple pendulum: Obtaining motion of pendulum bob from string tension time series

TL;DR

This paper investigates methods to derive pendulum bob motion from string tension data, revealing challenges due to quadratic terms and errors in reconstructed angular displacement.

Contribution

It presents a numerical procedure to estimate pendulum motion from tension data, highlighting its limitations and the impact of quadratic terms.

Findings

The proposed method cannot accurately recover pendulum motion due to quadratic term issues.

Applying the sign of tension yields positive-only displacement results.

Reconstructed angular displacement has an error of approximately 7.6%.

Abstract

Time series of string tension of a simple pendulum has not yet been a interesting motion information, even nowadays using a force tension sensor can be measured easily. A numerical procedure is presented how to obtain motion of pendulum bob from the string tension. Unfortunately, proposed procedure does not work. A quadratic term of \omega loses the sign of \omega that prevents the procedure to work. Applying sign of string tension into the procedure can produce the time series but only in positive value. The error for reproduced angular displacement is about 7.6%.