• 大学生园地 •

### 韦氏摆的弹性力学分析：圆柱螺旋弹簧模型的特色推导与验证

1. 天津大学理学院，天津300350
• 收稿日期:2021-11-30 修回日期:2022-04-26 出版日期:2023-02-20 发布日期:2023-02-17
• 通讯作者: 张福林,E-mail：flzhang@tju.edu.cn
• 作者简介:刘天恒（2002—）,男,浙江嘉兴人,天津大学理学院应用物理学（强基计划）2020级本科生
• 基金资助:
天津大学本科教育学改革研究项目（基于“力学”及“基础物理学A”课程的创造性学习模式的引导）资助

### The elastic analysis of Wilberforce pendulum: characteristic derivation  and verification of cylindrical spiral spring model

LIU Tian-heng，CAO Bo-xing, ZHANG Fu-lin

1. College of Physics，Tianjin University，Tianjin 300350，China
• Received:2021-11-30 Revised:2022-04-26 Online:2023-02-20 Published:2023-02-17

Abstract: 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.