Abstract: The aceurate processing of experimental data is essential in physics. However,experimentallymeasured data are often discrete and limited, presenting challenges in reconstructing the inherent continuity ofphysical processes. Consequently, investigating the applicability of various interpolation methods inreconstructing continuous curves across diverse physical scenarios emerges as a pivotal issue.In this study,fourinterpolation methods-linear,shape-preserving piecewise cubic,cubic Hermite,and cubic spline-are appliedto experimental data from three types of experiments:forced vibration, Franck-Hertz,and simple pendulum.Theresults show that shape-preserving piecewise cubic interpolation works best for forced vibration data, cubicsplineinterpolation is more suitable for the Franck-Hertz experiment,while the simple pendulum caseunderscores the limitations of interpolation methods under conditions of data sparsity and high noise levels.Collectively,'these findings support the central conclusion of this study: no single interpolation method isuniversally optimal,and the choice of an appropriate method depends critically on the intrinsic nature of thephysical experiment and the characteristics of the data obtained.
