威尔伯福斯摆的耦合运动研究

Research on the coupled vibrations of Wilberforce pendulum

威尔伯福斯摆(简称韦氏摆)由悬挂在竖直方向的螺旋弹簧和连接在弹簧末端的物块(摆锤)组成,它既能沿着弹簧上下振动,又能绕竖直轴旋转.本文从力学角度分析了韦氏摆的竖直振荡与水平振荡振幅随时间发生强弱周期性变化的原因,从分析力学的角度对韦氏摆竖直振荡和水平振荡的运动过程进行了理论分析,分析了影响韦氏摆耦合运动状态的因素,并实验探究了转动惯量对韦氏摆耦合状态的影响,发现随着转动惯量的增加,韦氏摆呈现三种运动状态,即强耦合、弱耦合、近似不耦合.采用控制变量法探究了弹簧初始伸长量对韦氏摆运动的影响,实验结论与理论分析吻合.

Wilberforce pendulum is composed of a vertical spiral string and a pendulum bob fixed on the bottom of the string, it can vibrate vertically and rotate back and forth horizontally. In this paper, the reason why the amplitude of vertical oscillation and horizontal oscillation changes periodical is analyzed experimentally from the perspective of mechanics, and the motion of vertical oscillation and horizontal oscillation of Wilberforce pendulum from the perspective of analytical mechanics. The factors affecting the coupled motion state of Wilberforce pendulum are analyzed, and the experiment is used to study the influence of moment of inertia of Wilberforce pendulum on the coupled motion state. Wilberforce pendulum undergoes three motion states with the increase of moment of inertia: strong coupling, weak coupling and approximate decoupling. control variates are used to study the influence of the initial elongation of the string on the motion of Wilberforce pendulum. The results are in good agreement with the theoretical analysis.