Re: fallacious filtered white noise

[Andy Dougherty <doughera@LAFAYETTE.EDU>]

On Sat, 9 Dec 2000, Michael Edmiston wrote:

> There is an experiment I have students do that is simple to perform, but
> gives complicated results.  I hang a spring pendulum from an electromagnetic
> driver.  The driver is run by a sine-wave oscillator, and the students note
> the behavior of the spring pendulum when the driver frequency is near the
> natural frequency of the spring pendulum.  I use the Pasco-scientific
> SF-9324 driver with a spring pendulum having m = 10g, k = 0.515, T = 0.767
> s, f = 1.304 Hz.

I have done a similar experiment horizontally in the following way: Place
an air track glider at the center of the air track

    ______                                              ______
          |                                             |
          |---- spring ------ [glider] ------ spring ---| Driver
          |                                             |
    ______]_____________________________________________[_____
    ______]________________Air Track____________________[_____

Then, to get some damping, place two strong flat magnets on either side
of the glider.  (Place them symmetrically to maintain balance.) You
will get eddy-current damping.  Adjust (fiddle) with the placement of
the magnets so that the damping is moderate.  You want a compromise
between the weak damping usually assumed in the analysis and the finite
patience of your students in waiting for transients to die out.  I
typically aim for a "half-life" of about 5 to 10 oscillations.  That
is, in the unforced case, I adjust the magnets until it takes about 5 ~
10 oscillations for the amplitude to decay to about 1/2 of its original
value.

This seems to work fairly well.  There are still significant problems
with the non-sinusoidal driving (as well as the other feedback
problems mentioned.)

    Andy Dougherty              doughera@lafayette.edu
    Dept. of Physics
    Lafayette College, Easton PA 18042