Experimental Study of Gravity Measurement with a Video-Based Laboratory Pendulum with Tracker Software: Comparison of Weighted and Unweighted Tests

This research aims to determine the value of the Earth's gravitational acceleration (g) using the mathematical pendulum swing method with an unweighted linear regression approach, weighted linear regression, and the 4th-order Runge-Kutta numerical method. The data used are the results of measuring the swing period of the pendulum for various lengths of string. The analysis was carried out by calculating the average value of gravitational acceleration using multiple methods. The results show that weighted linear regression provides more consistent and accurate estimates than unweighted linear regression, with a high coefficient of determination (R²) value. The Runge-Kutta numerical method is also used to predict swing periods with a more in-depth mathematical approach, producing values ​​supporting experimental data trends. Overall, this research makes an average value of gravitational acceleration of around 9.11 m/s², close to the expected theoretical value. These findings show that the mathematical pendulum swing method can be used effectively to measure the Earth's gravitational acceleration with sufficient accuracy and provide an essential contribution in the context of physics education regarding the application of basic principles in physics experiments.