耦合摆的受迫有阻尼振动研究

摘要：耦合摆是由两个完全相同的平行悬挂的单摆，两个摆锤之间由一根轻质弹簧相连接而构成。我们可以直观地把物体间的耦合振动现象体现出来。观察到普遍存在于耦合系统的“拍”现象，并通过其物理模型对其进行理论分析。耦合摆的“拍”现象普遍存在于光学系统、天体系统、机械振动系统、固体晶格中相邻原子的振动模型、地铁工程、阻尼机械部件等人造或天然系统中。了解并研究“拍”现象的基本特征、产生的条件和教学演示设计，对物理教学具有重大的理论以及现实意义。经过一系列计算研究可得知，耦合摆在无阻尼条件下，两个单摆的振动均是两个简谐振动的叠加；在有阻尼条件下，与无阻尼情况下相比，多了一种与阻尼因子有关的衰减项，阻尼因子的不同将使得耦合摆做更复杂的过阻尼及欠阻尼振动；在受迫有阻尼的情况下，耦合摆的振动情况与策动力有关，当策动力频率处于两固有频率之一附近时，产生共振，由于策动力直接施加在第一个振子上，所以此振子的振幅较大，而第二个振子只是间接受到策动力的作用，因此振幅较小，振幅较平缓。85451

毕业论文关键词：耦合摆，振动，“拍”现象，受迫，阻尼

Abstract：Coupled pendulum is consisted of two identical simple pendulum that suspend parallelly 。 They are linked by a light spring。 We can reflect the coupled vibration between the objects intuitively and observe the “beat” phenomenon which exists generally in the coupled system。 Then doing theoretical analysis through its physical model。 The coupled pendulum’s “beat” phenomenon generally exists in the optical system, sphere systems, mechanical vibrating system, adjacent carbon atom’s model of vibration in solid lattice, subway engineering, damping of mechanical parts and other man-made or natural systems。 Learning and researching “beat” phenomenon’s essential features, producing condition and the design of teaching demonstration have great theoretical and realistic significance for physics teaching。After a series of calculation, results indicated that, in the absence of coupled pendulum damping conditions, the vibration of two pendulum are the superposition of two harmonic vibration; under damped conditions, compared with no damping, a damping factor associated with the decay, the damping factor will make different coupling to do a more complex damping and damping vibration; the forced damped case, vibration coupled pendulum associated with driving, when the driving frequency is near one of the two natural frequency, resonance, the driving force is applied directly to the first oscillator, the oscillator amplitude is large, while the second oscillator only to the driving effect, so the amplitude will be smaller and gently。源Q于W优H尔J论K文M网WwW.youeRw.com 原文+QQ75201.,8766

Key Words：coupled pendulum, vibration, “beat” phenomenon,forced, damping

1 前言 4

1。1相关介绍 4

1。2相关运用和体现 4

1。3研究过程及求解方法 4

2 实验装置 5

3 耦合摆振动的研究 6

3。1 耦合摆的无阻尼振动 6

3。2 耦合摆的有阻尼振动 10

3。3 耦合摆的受迫有阻尼振动 13

结论 16

参考文献 17

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