3a75.10 Six Coupled Oscillators

PURPOSE: To show the normal modes for a mechanical system comprised of six coupled masses and springs, and to show the transient response and the steady state response for each mode.

DESCRIPTION: The airtrack has a system of six equal gliders connected by equal springs as shown in the above photo.   The system is driven into oscillation with a mechanical vibrator controlled by a function generator.  Each normal mode, and the transient response and the steady state response for each mode can be shown by applying the appropriate harmonic frequency to the driver. 

Note: The period for each mode is quite low, about 1 second.  It takes the application of many periods before the transient response fades and the steady state reaches its amplitude and mode of oscillation.  Therefore, it takes some amount of classtime time to show an individual mode.  This is not a quick and easy demo.   Since there are 6 modes, and it can take up to 1/2 hour to demonstrate all the modes of the system.  Please consider the necessary class time needed to show two or three modes.   Also, note that the Q, the quality factor, is very high for the resonance of this system.  Therefore, the frequency of each mode must be tuned PRECISELY to achieve the mode.

EQUIPMENT:  Airtrack with 6 gliders and 7 springs, mechanical vibrator and function generator, as photographed.

SETUP NOTES: The 7 springs are identical, and the six masses have thier weights matched using Apeizon Q wax to equal 200 g.