Experiment

To test these theoretical predictions, we placed two equal-mass gliders (0.233kg) on a 2m long airtrack and connected the gliders with springs (N/m). The outer springs were chosen to be as identical as possible, for otherwise forces Eqs. (1) and (2) would not be valid, and the normal modes are not the highly symmetric ones described above. There is no restriction on the spring constant of the inner spring.

A small card was placed on the left-hand glider (glider 1) to give a good sonic reflection, and only the displacement of this glider was measured. The measurements were made with a typical MBL[4] setup:

1. An ultrasonic ranger, which measured the distance to the card 50times/s,
2. A Universal Lab Interface (ULI) which processes the time-delay signals and communicates to the host computer,
3. A Macintosh LC III computer with floating-point coprocessor, and
4. MACMOTION and Microsoft EXCEL software for data analysis and simulation.

The normal modes are easy to observe: if you pull both gliders about 5cm to the right and let them go simultaneously, you see a simple periodic motion, which is the symmetric mode. The upper portion of Fig. 3 shows the motion of glider 1, with a frequency of 0.596Hz.

The antisymmetric mode is equally easy to observe: displace the gliders equal amounts in opposite directions and release them from rest. The lower portion of Fig. 3 shows the motion of glider 1, with a frequency of 1.044Hz.

We can also have much more complicated motion. For example, if we displace glider 1 by -7.5cm, keep glider 2 at its equilibrium position, and release both from rest, we get the very complicated motion shown in the upper panel of Fig. 4. This motion is clearly not simple harmonic motion, and shows the general complexity of the coupled oscillators.