Abstract: The snake pendulum is a classical mechanics demonstration device composed of multiple simplependulums with different lengths, holding significant value in applied physics experimental teaching at localuniversities. To address the limitations of traditional small-angle (<5o) approximations where the oscillationamplitude is too small and demonstration effects are restricted, this study establishes an exact dynamic model ofthe snake pendulum based on MATLAB, systematically investigates its nonlinear characteristics, and developsteaching extension designs. First, the exact period formula for large-angle oscillations based on the completeelliptic integral of the first kind is derived, and a snake pendulum system comprising 10 pendulum bobs with atotal period of 40 s is designed. To meet demonstration requirements with pendulum angles expanded from 5o to45o, two implementation schemes-" period compensation" and " pendulum length compensation"-areproposed. Theoretical calculations indicate that when the pendulum angle increases to 45o, adopting the periodadjustment scheme(new period 41.598 9 s) can enlarge the maximum horizontal oscillation amplitude of thebobs from 6.54 cm to 53.07 cm without requiring reprocessing of pendulum lengths, significantly enhancingexperimental operability. MATLAB numerical simulations verify the periodicity and waveform evolution patternsof different pendulum bob positions over time, providing effective theoretical guidance and practical solutionsfor physics experimental teaching.
何春乐, 付美荣. 蛇形摆的 ＭＡＴＬＡＢ 模拟及拓展研究[J]. 大学物理实验, 2026, 39(4): 73-77.
HE Chunle, FU Meirong. MATLAB Simulation and Extended Research of the Snake Pendulum. Physical Experiment of College, 2026, 39(4): 73-77.
