Well, I went to that link and immediately thought of the physics lab at the Univ of Oregon, where my son works. He recently took me on a behind-the scenes tour and showed me the demo with the highest "simplicity versus coolness factor" that they have. It's just a chunk of metal shaped like a yoke from a car u-joint (like a small pipe cross except solid metal) hanging from a spring. Pull it straight down, let go and it bounces up and down, up and down... and pretty soon the "yoke" begins to rotate back and forth a little while bouncing up and down, then a little more, and soon the vertical motion completely stops, and this little yoke is winding up and unwinding that spring like the mechanism in an old clock, then the vertical motion begins, and gets bigger and the spinning slows... It was entrancing, and I thought it was the best ever exhibit!
Until today... boy could they wake up the sleepyheads in physics 101 with that demo you linked to!
Here's another one: on my car ('95 Ford Contour), if I pluck the radio aerial, it swings back and forth in a plane at first, then the end starts describing an elliptical motion until it's eventually vibrating in a plane perpendicular to the one it started in, then the process reverses.
I *think* what's going on is that the aerial might be slightly elliptical so it has slightly different resonance frequencies in the different directions,
Gotta find a spring and try that yoke trick.......
Nope. Coupled resonances. Gauranteed to happen. Don't know if you saved it but we had that discussion back in May '02. I set it up in APL and sent you the graphs. I'll send it agian if you like. If you want to duplicate it in MathCAD (that's the one you have isn't it) just set up a Runge-Kutta solution for two identical SHM's and run it with initial conditions to start one but not the other. This is to convince you that there is no coupling yet. Now add a _small_ amount of the displacement of each to the other and plot again. You will see the described phenomenum.
Then when you make the physical one, you'll know how to explain it! :-)
My favorite example is coupled pendulums. A pendulum exhibits approximately SHO behavior.
Take a string and stretch it horizontally taught. Suspend two weights from strings attached to the first string making two pendulums. Start one pendulum swinging and watch the energy transfer to the other pendulum and back. The pendulum that starts swinging will be a quarter cycle ahead of the other pendulum. When the first pendulum comes to rest, it pauses to let the other pendulum get a quarter cycle ahead.
I haven't found a web reference yet for the oscillating yoke/cross, but I'll have my son take pictures, then I'll post them in the drop box after MLK day.
Or, were you referr>OK, any references to that experimental item that we can go to?
Coupled pendulums are nice, and so are chaotic pendulums. Here are directions for a small chaotic pendulum; scale up as desired.
From .5"x.2" aluminum bar, cut a 4" piece and a 6.5" piece. At A and B (see diagram) drill holes for press fit of .250"-diameter roller bearing; at C, drill for press fit of a shaft. A B C --------------------------- -------------- |o o| |o | --------------------------- -------------- Make an 11"-high stand and attach a shaft through bearing at A. Attach a shaft from C through bearing B.
Now give the coupled bar a push. As the long bar spins around A and the short bar around B, from time to time the short bar will do strange flips, reverse direction, start and stop, etc.
The bearings I used came out of old disk drives. They have short stub shafts tightly pressed into the inner race, and work ok for this thing without modification.
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