智能手机揭示的威尔伯福斯摆的耦合振荡
Coupled oscillations of the Wilberforce pendulum unveiled by smartphones
摘要：
威尔伯福斯摆是一个伟大的经验，说明耦合振荡系统的重要性质，如正常模式和拍现象，在物理课程。连接到质量的螺旋弹簧组成了这个简单但丰富多彩的设备，它具有纵向和扭转振荡的特点，吸引了学生和教师的目光，并提供了一个梦幻般的环境来定性和定量地研究耦合振荡。然而，通常用于同时获取两种振荡类型的实验设置可能是麻烦的和/或昂贵的，通常需要两个同步的相机，或运动传感器和光电门，由昂贵的模数转换器集成。在这里，我们表明，智能手机可以成为记录威尔伯福斯钟摆振荡的完美设备，该钟摆仅由一个教育螺旋弹簧和一个罐子组成。我们的设置采用智能手机的加速器和陀螺仪分别从纵向和扭转振荡中获取数据。此设置可以成功记录正常模式和心跳。此外，我们表明，我们的实验获得的时间序列和功率谱是在很大程度上与模拟的运动方程。此外，我们批判性地分析了如何设置初始条件，以观察正常模式和拍。我们相信，我们的研究有助于使威尔伯福斯钟摆的惊人物理学更接近本科课堂，具有低成本，高可用性的材料。
英文摘要：
The Wilberforce pendulum is a great experience for illustrating important properties of coupled oscillatory systems, such as normal modes and beat phenomena, in physics courses. A helical spring attached to a mass comprises this simple but colorful device that features longitudinal and torsional oscillations, catching the eye of students and teachers, and offering a fantastic environment to study coupled oscillations at qualitative and quantitative levels. However, the experimental setups that are commonly used to simultaneously acquire both oscillation types can be cumbersome and/or costly, often requiring two synchronised cameras, or motion sensors and photo-gates integrated by an expensive analog-to-digital converter. Here, we show that a smartphone can be the perfect device for recording the oscillations of a Wilberforce pendulum composed of just an educational helical spring and a can. Our setup employs a smartphone's accelerator and gyroscope to acquire data from the longitudinal and torsional oscillations, respectively. This setup can successfully record both normal modes and beats. Furthermore, we show that our experimentally obtained time-series and power spectra are in great agreement with simulations of the motion equations. In addition, we critically analyse how to set the initial conditions to observe both normal modes and beats. We believe our study contributes to bring the striking physics of the Wilberforce pendulum closer to undergraduate classrooms with low-cost, highly-accessible materials.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
