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

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%.