【摘要】 本文对2022年IYPT的一道题目“橡皮筋上的球”进行了研究，在对橡皮筋扭转力和阻尼作线性假设的条件下，建立了二自由度线性阻尼自由扭振模型描述双球橡皮筋运动规律，建立了弹性圆轴的剪切形变力学模型描述橡皮筋的力学性质，并给出解析解。本文解释了双球橡皮筋系统的“钟摆”行为，定量探究了此行为与相关参数的依赖关系；通过Tracker软件得到了相关实验数据，验证了模型的正确性，并对实验中的等时性破缺现象进行了半定量解释，对非线性公转半径r随时间t的变化进行了定性分析。更多还原

【Abstract】 A topic of 2022 IYPT “Balls on an Elastic Band” is studied. Under the condition of linear assumption of torsion force and damping of rubber band, a two-degree of freedom linear damping free torsional vibration model is established to describe the motion law of elastic band with double ball. A shear deformation mechanical model of elastic circular axis is established to describe the mechanical properties of elastic band, and the analytical solution is given. The pendulum behavior of the double ball rubber band system is explained, and the dependence between the behavior and the related parameters is explored quantitatively. The Tracker software was used to obtain relevant experimental data to verify the correctness of the model. The constant period breaking phenomenon in the experiment was explained semi-quantitatively, and the change of the nonlinear revolution radius r with time t was analyzed qualitatively.更多还原