Direct measurement of the normal coordinates in a system of coupled oscillators

"Direct measurement of the normal coordinates in a system of coupled oscillators"
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Álvaro Suárez*, Daniel Baccino†, Martín Monteiro‡, Arturo Martí§
* CFE-ANEP, Montevideo, Uruguay. (alsua@outlook.com)
† CFE-ANEP, Montevideo, Uruguay. (dbaccisi@gmail.com)
‡ Universidad ORT Uruguay. (monteiro@ort.edu.uy)
§ Instituto de Física, Facultad de Ciencias, UdelaR, Uruguay. (marti@fisica.edu.uy)

Abstract
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 mass of the springs is relatively small compared to that of the gliders, when it is taken into consideration agreement with the experimental results is appreciably improved.

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