Simple Harmonic Motion

erco

And now for something completely different:

A beautiful demo of several pendulums swinging slightly out of phase. Hard to believe it cycles through all that and comes back to a nearly perfectly synchronized start position, but the video looks legit to me. Must have taken quite a while to calibrate all of those string lengths.

Heater.

That's a very nice demo. No reason it should not be legit. It's only a bunch of oscillators at slightly different frequencies going in and out of phase with each other.

A slightly more surprising experiment is "coupled harmonic oscillators" where energy is transferred back and forth between two pendulums each one coming to rest at regular points in time whilst all the energy in the system causes the other to have maximum amplitude.

As in this nice demo by the wonderful Professor Roger Bowley http://www.youtube.com/watch?v=izy4a5erom8

You can make coupled oscillators with two resonant LC tank circuits where a week coupling between the inductors transfers the energy from tank to tank. It's kind of fun to set that up in a SPICE simulation as well.

Lev

and a similar demo...made of plywood

http://www.arborsci.com/pendulum-wave

Check out the video about 2/3 down the page

Martin_H

I've seen that demo before, but the darkness coupled with the lighting make it especially clear. If you watch a single pendulum, you'll notice that it swings at a constant rate. The coming in and out of phase is because the period of the shorter ones are multiples of the longer ones.

Duane Degn

Martin_H wrote: »

The coming in and out of phase is because the period of the shorter ones are multiples of the longer ones.

I don't think the quite it. The slowest period isn't too far off from the fastest. I think the ratio between the various periods are made up of reasonably sized whole numbers which allow the phases to realign every so often.

If I had seen this demo before I had done my 32 servo demo, I would attempted something like this as part of the demo. As it was, I did have the servos move each a bit out of phase from the others to give a bit of a wave motion.

I'm sorely tempted to rig up 12 servos with sticks and fluorescent balls to give this a try with servos. I think the software would be trivial (by reusing the 32 demo code) but I'm not keen on putting the hardware together.

As much as I like watching servos move, I think a demo like this with servo would loose a lot of the mystic supplied by real pendulums.

erco

Duane Degn wrote: »

I'm sorely tempted to rig up 12 servos with sticks and fluorescent balls to give this a try with servos. I think the software would be trivial (by reusing the 32 demo code) but I'm not keen on putting the hardware together.

As much as I like watching servos move, I think a demo like this with servo would loose a lot of the mystic supplied by real pendulums.

You chicken, McFly?

Martin_H

Duane Degn wrote: »

I don't think the quite it. The slowest period isn't too far off from the fastest. I think the ratio between the various periods are made up of reasonably sized whole numbers which allow the phases to realign every so often.

When I say a multiple I wasn't thinking integer multiples. I was thinking along the lines of strings on a musical instrument. The string an octave lower is a multiple of 2 of the higher octave string, while strings between the two octave string are a fractional multiple greater than 1, but less than 2.

Circuitsoft

Try this one:

Go to http://www.falstad.com/circuit/ and on the pop-up, go to File->Import and paste:

$ 1 5.0E-6 10.20027730826997 50 5.0 50
R 160 160 112 160 0 0 40.0 5.0 0.0 0.0 0.5
r 224 160 288 160 0 100.0
c 288 160 288 208 0 1.0E-5 5.0
g 288 208 288 224 0
w 288 208 336 208 0
w 288 160 336 160 0
c 464 160 464 208 0 1.0E-5 -6.907369909148394E-4
g 464 208 464 224 0
s 160 160 224 160 0 1 false
T 336 160 416 208 0 0.1 1.0 5.450899798339537E-6 5.450899798339523E-6 0.1
w 416 208 464 208 0
w 416 160 464 160 0
r 336 160 336 208 0 10000.0
r 416 160 416 208 0 10000.0
o 2 64 0 34 0.00244140625 9.765625E-5 0 -1
o 6 64 0 34 0.00244140625 9.765625E-5 0 -1

W9GFO

Reminds me of this demo;