本文建立了威尔伯福斯摆上下振动与扭转摆动耦合共振的数学模型，并分析了其相关影响因素；通过搭建实验系统，用PASCO传感器观测其运动模式，基于控制变量法进行了探究.研究结果表明，摆上下振动和扭转摆动之间存在共振性的能量转化，摆锤的转动惯量会对其运动状态产生影响，且两种运动的耦合导致了“拍”现象的出现.

In this paper, a mathematical model of the coupled resonance between the up-and-down vibration and torsional swing of the Wilberforce pendulum is established, and its related influencing factors are analyzed. By building an experimental system, the motion mode of the Wilberforce pendulum is observed with the PASCO sensor, and the research is carried out based on the control variable method. The research results show that there is a resonant energy conversion between the up-and-down vibration of the pendulum and the torsional swing, and the rotational inertia of the pendulum will affect the motion state of the pendulum, and it is concluded that the coupling of the two motions leads to the “beat” phenomenon.