耦合振子系统的简正坐标及弹簧质量的影响
Normal coordinates in a system of coupled oscillators and influence of the masses of the springs
摘要：
对任意初始条件下的两耦合振子系统的运动进行了实验分析，直接得到了系统的法向坐标。该系统包括两个滑翔机在空气轨道上移动，通过弹簧连接在一起，并通过另外两个弹簧连接到固定端。通过对实验数字视频的分析，获得了物体的质心位置和相对距离，得到了物体的法向坐标，并通过非线性拟合得到了物体的固有频率。结果表明，虽然质量的弹簧是相对较小的相比，滑翔机，它是必要的，考虑到提高与实验结果的一致性。这个实验理论的建议是针对一个本科实验室。
英文摘要：
Experimental analysis of the motion in a system of two coupled oscillators with arbitrary initial conditions was performed and the normal coordinates were obtained directly. The system consisted of two gliders moving on an air track, joined together by a spring and joined by two other springs to the fixed ends. From the positions of the center of mass and the relative distance, acquired by analysis of the digital video of the experiment, normal coordinates were obtained, and by a non linear fit the normal frequencies were also obtained. It is shown that although the masses of the springs are relatively small compared to that of the gliders, it is necessary to take them into consideration to improve the agreement with the experimental results. This experimental-theoretical proposal is targeted to an undergraduate laboratory.
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