摘要
同步行为是自然界普遍存在的现象.若干个机械节拍器于某些特定条件下,分别给各个节拍器的摆以任意的初始相位,一段时间后各个摆会达到同步的运动状态.本文首先通过分析节拍器的内在工作机制建立了单个节拍器的动力学方程,根据实验结果给出了动力学方程中的阻力矩和动力矩随时间变化的规律,然后引入惯性力,表示节拍器之间的耦合作用,建立了节拍器系统的动力学方程,物理意义清晰,能够较好地解释平行摆放在水平木板上具有相同摆动周期的节拍器的同步现象.通过与实验的对比发现理论可以较好地预测节拍器系统达到同步的时间,并且在不同实验条件下体现出良好的普适性.
Synchronous behavior is a ubiquitous phenomenon in nature. Under certain conditions,a number of mechanical metronomes,which are given an arbitrary initial phase,will reach the synchronized state of motion after a period of time. In this paper,firstly,we establish the dynamic equation of a single metronome by analyzing its internal working mechanism.According to the experimental results,the laws of the change of the resistance moment and the dynamic moment with time are given.Then the coupling action between the metronome is represented by the inertial force,so the dynamic equation of the metronome system is established with much more clear physical meaning which can better explain the synchronization phenomenon of the metronomes with the same swinging period on the horizontal board.The theory can be used to predict the time of the metronome system to achieve the synchronization,meanwhile,this theory model shows the good universality under different experimental conditions.
引文
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