失谐耦合摆运动规律的研究

摘要

We theoretically studied the motion of the detuning coupled pendulums using Lagrange method,and experimentally measured the influence of slope factors ε on the pendulums’ angular frequencies. The results prove that the pendulums’ frequencies have the larger variation asε <0 thanε >0 and their vibrations can be controlled continuously through changing the slope of spring. Base on these results,we discussed the law of mo-tion of detuning coupled pendulums under two inclined springs actions,and found the detuning coupled pendu-lums can be back to resonance again as two slope factors meet the appropriate conditions. These results in this paper are helpful for designing new resonance devices and meanwhile afford a new way to control resonance.%本文利用拉格朗日方法，理论上分析了失谐耦合摆的运动规律，并从实验上观测了弹簧的倾斜因子ε对双摆振动角频率的不同影响，确定了弹簧向下偏离平衡位置时较向上偏离时对两摆角频率的影响大，通过改变弹簧的倾斜因子可以连续调节摆的振动规律。在此基础上，研究了双倾斜弹簧连接双摆时对双摆运动规律的影响，发现当倾斜因子ε1、ε2满足一定关系时，两根失谐弹簧作用的耦合摆振动等效于标准耦合摆振动规律。在实际应用上，可以借助双根弹簧共同调节和稳定耦合振动仪表，提高测量精度。