转速对固有频率的影响：想象的“反重力”世界的简短介绍和演示
Influence of rotation speed on natural frequency: A short introduction and presentation of an imaginary 'antigravity' world
摘要：
我们提出了一个有启发性的方法来介绍使用一个典型的弹簧质量系统的共振的主题没有阻尼。与大多数教科书中的标准方法相反，在这里，我们提出了一种方法，将讲座从常见的平移系统扩展到旋转系统。在后一种情况下，特别注意变量向心力的作用。学生将找到最简单的运动常微分方程的解析解，并看到固有频率强烈依赖于转速，后者是一个简单的矢量和。分析表明，地面合力总是简谐的。为了描述旋转对固有频率的影响的意义，我们提出了一个想象的“反重力”世界，其中没有上述的依赖性。
英文摘要：
We present an instructive way to introduce the subject of resonance using a typical spring-mass system without damping. In contrast to the standard approach found in most textbooks, here we propose a way to extend the lectures from common translational systems to rotating ones. In the latter case, particular attention is paid to the role of the variable centripetal force. The students will find analytical solutions of the simplest possible ordinary differential equations of motion and see that the natural frequency strongly depends on the rotation speed, the latter being a simple vector sum. The analysis reveals that always the resultant ground force is harmonic. In order to depict the significance in the influence of rotation on natural frequency, we present an imaginary 'antigravity' world in which the aforementioned dependency is absent.
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