On the use of local fitting techniques for the analysis of physical dynamic systems

In this paper, we propose the use of local regression techniques to analyse experimental data in the graduate physics laboratory. These techniques allow a better understanding of the system dynamics, based on the estimation of both the system response and its derivatives, by using an adaptive weight function. This method provides a comprehensive analysis of the governing differential equation. Local polynomial fitting presents several advantages over conventional adjustment methods, such as a better sensitivity to small model deviations and the possibility of analysing local aspects. Moreover, phase space representation is employed for analysing the system dynamical behaviour. Additionally, the students are confronted with an alternative point of view, very useful in experimental data exploration and result interpretation. The proposed methodology is demonstrated with the analysis of electric oscillations in an RLC circuit.