韦氏摆又称威尔伯福斯摆，是一种特殊的耦合摆，由竖直悬挂的圆柱螺旋弹簧和固连在弹簧末端的物块组成.物块有两个自由度：沿弹簧轴线拉伸的位移，绕弹簧中轴线扭转的角位移，在运动时，物块的平动动能和转动动能会发生周期性转化. 本文研究了IYPT2021第12题的韦氏摆，给出了系统的拉格朗日函数，得到了描述耦合现象的运动方程.利用圆柱螺旋线的自然坐标系，建立了圆柱螺旋弹簧模型.从弹性力学角度出发，进行了微元分析,将圆柱螺旋线的曲率和挠率变化的几何意义与弹簧材料应变的物理意义联系，得到了弹簧弹性势能的解析解.其数学计算是严格的，具有一定的普遍性，可推广应用于各类与均质弹簧力学有关的精密计算.文中还进行了静力学实验，弹性系数的理论值落在实验值合成标准不确定度的范围内，验证了圆柱螺旋弹簧模型的正确性.

The Wilberforce pendulum is a special coupled system,which is a combination of a vertically suspended cylindrical helical spring and an object fixed at the end of it. The block has two degrees of freedom: the displacement stretching along the central axis of the spring the angular displacement twisting around the central axis of the spring. Its translational kinetic energy and rotational kinetic energy can transform periodically during the viberation at a special set of parameters. The Wilberforce pendulum in question 12 of iypt2021 is studied. In this work，the Lagrange function of the system is given, and the motion equation describing the coupling phenomenon is obtained. Using the natural coordinate system of cylindrical helix, the model of cylindrical helix spring is established. From the perspective of theory of elasticity, the spring model is analyzed by microelement. The geometric meaning of the curvature and torsion of the cylindrical helix is connected with the physical meaning of the spring material strain, and the analytical solution of the spring elastic potential energy is obtained. The mathematical calculation of this method is strict and universal, and can be extended to all kinds of precision calculation related to homogeneous spring mechanics. The static experiment is also carried out, and the theoretical value of the elastic coefficient falls within the range of the synthetic standard uncertainty of the experimental value, which verifies the correctness of the cylindrical coil spring model.