论文标题

Wilberforce Pendulum的耦合振荡由智能手机揭示

Coupled oscillations of the Wilberforce pendulum unveiled by smartphones

论文作者

Gallot, Thomas, Gau, Daniel, García-Tejera, Rodrigo

论文摘要

Wilberforce钟摆是一个很好的体验,可以在物理课程中说明耦合振荡系统的重要特性,例如正常模式和Beat现象。质量上的一个螺旋弹簧包括这种简单但丰富多彩的设备,具有纵向和扭转振荡,吸引学生和老师的眼睛,并提供了一个奇妙的环境,以在定性和定量水平上研究耦合的振荡。但是,通常用于同时获取这两种振荡类型的实验设置可能很麻烦和/或昂贵,通常需要两个同步摄像机,或者由昂贵的模拟数字转换器集成的运动传感器和光门。在这里,我们表明智能手机可以是录制Wilberforce Pendulum的振荡的理想设备,该摆锤仅由一个教育的螺旋弹簧和罐子组成。我们的设置使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节拍。此外,我们表明我们实验获得的时间序列和功率谱与运动方程的模拟非常一致。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节拍。我们认为,我们的研究有助于使Wilberforce钟摆的惊人物理学更接近具有低成本,高度访问材料的本科教室。

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.

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