Enhancing measurement accuracy in Kater's pendulum experiments via an AI-assisted virtual laboratory

Abstract

Abstract

This study identifies and rectifies a systematic deficiency in existing virtual Kater reversible pendulum experiments: the equal-period condition T1 = T2 is conventionally located by visual inspection of discretely sampled data, introducing a worst-case grid-selection error of up to approximately 0.08% in the calculated gravitational acceleration. The work makes three contributions. First, a linear interpolation algorithm is embedded within a Python/Streamlit web application to replace manual estimation with a reproducible numerical procedure, reducing the discretisation error to below 0.002% - a forty-fold improvement. Second, a sensitivity analysis over sampling steps of 0.5–5.0 mm confirms that the original 1 mm step of the HCMUTE simulation is adequate, with errors rising to 0.064% only at 5 mm. Third, a retrieval-augmented AI tutor is integrated to guide student reasoning without supplanting the physical model. The framework generalises to any experiment that requires locating a characteristic point in discrete data.