Dynamics of a physical pendulum with a magnet in the presence of a coil

Abstract We investigated the dynamics of a wood physical pendulum, supported by a PVC structure and having a magnet glued to its oscillating end and whose oscillation occurred in the vicinity of a coil that was sometimes in short-circuit, sometimes in open-circuit. The pendulum trajectory, position as a function of time, was drawn with the aid of frame-by-frame video analysis, helping to detect a greater damping of the oscillation in the presence of the coil in short-circuit. The equations of motion for the pendulum were modeled and solved, showing to be satisfactory to describe the observed dynamics and, thus, used to make an interesting prediction of interaction between the permanent and induced magnetic fields in the case of an analogous system to be built with distinctive construction characteristics (reduced moment of inertia and increased magnet field). We hope that the work can serve as a stimulus to quantitative investigations of simple systems and will motivate the significant learning of Mechanics and Electromagnetism.

摘要：本研究针对一款木质物理摆展开动力学特性分析。该摆由聚氯乙烯（PVC）结构支撑，摆动末端粘贴有一块永磁体，其摆动区域附近设有一个可切换为短路（short-circuit）或开路（open-circuit）状态的线圈。通过逐帧视频分析（frame-by-frame video analysis）方法，绘制得到该摆的运动轨迹——即位置随时间的变化关系，借此可观测到线圈处于短路状态时，摆的摆动阻尼显著增大。本研究为该物理摆建立了运动方程（equations of motion）并完成求解，结果表明该模型能够较好地描述观测到的动力学行为；基于此，可针对一类具备独特结构特征（更小的转动惯量（moment of inertia）与更强的磁场）的待搭建同类系统，对永磁场（permanent magnetic field）与感应磁场（induced magnetic field）间的相互作用作出富有意义的预测。我们期望本研究能够为简单系统的定量研究提供启发，并助力学习者深入掌握力学与电磁学知识。