论文标题
共振曲线是完美的圆圈
Resonance curves are perfect circles
论文作者
论文摘要
接近物理现象并掌握其主要重要性的能力是一种非凡的理解质量。本文介绍了一种相当优雅，新颖的方式来研究共鸣现象，其中包括在各个物理领域都有共同的概念基础。为了简单起见，讨论将仅限于串联RLC电路中电流共振的情况。 因此，对电共振的数学进行了精心扩展，以至于它最终以一定的驱动频率与共振频率下的电流之间的宝贵关系。进一步，它引起了任何两个驱动频率之间的详尽相关性，这些驱动频率给出了相同的电流。 由前面提到的关系引起的，设计了一种新技术，这是一种简单的几何结构，而无需进行乏味的计算，就可以在任何给定频率下计算电流和印象深刻的电压之间的相位差。更不用说另一个几何实用程序是奇迹般地构造的，以将任何频率与其相应的``con轭''相关联，它允许电路中的相同电流。
The ability to approach a physical phenomenon and grasp its major importance is a remarkable quality of understanding. This paper presents a rather elegant and novel way of looking at the resonance phenomenon, which among others shares a common conceptual basis in various fields of physics. For the sake of simplicity, the discussion will be restricted to the case of electric current resonance in series RLC circuits. The mathematics of electric resonance is thus meticulously extended to the extent that it ultimately unravels an invaluable relationship between the current at a certain driving frequency and that at the resonance frequency. Much further it gives rise to an elaborate correlation between any two driving frequencies that give the same current. Arising from the previously mentioned relations, a new technique is devised, a simple geometrical construction, that without running into tedious calculations, allows the computation of the phase difference between the current and the impressed voltage at any given frequency. Not to mention another geometric utility, that is miraculously constructed to correlate any frequency with its corresponding ``conjugate'' one, that allows the same current in the circuit.
