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Pendulum experiments and resonant modes, and more

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Marko

Wed Oct 22 2008, 10:48PM

Registered Member #89 Joined: Thu Feb 09 2006, 02:40PM
Location: Zadar, Croatia
Posts: 3145

Hi all.

It began with me pondering with some coupled parallel LC circuits, with only limited knowledge. One day I had to write something up about air cored transformers, and I got to wiring a storage scope to both the transmitter and receiver coils.

After short time, I spotted something that seemed bizarre to me at that time - in some cases, voltages on tanks were in phase, and in other, 180 degrees out of phase! (which I had hard time understanding at first!)
Actually I was looking at the two different resonant modes of the fourth order system, each with their unique frequency and phase shift!

Two for me most unexpected pictures yet:

Only then I realized what's going on, and also finally understood the whole thing DRSSTC experts were talking about, that energy can be transferred with 180 degree shift as well...

But I also noticed even stranger phenomena, something I could call 'mode hopping' (or are mode locking actually proper words??);

By some tuning, I could get the system to the edge of in-phase mode, and then by slight lowering the coupling make it ''jump out'' of it into 180 deg. shift - with hysteresis! No matter how much coupling is increased again, I couldn't get the first mode back unless I cycle the power or re-tune!
I didn't have an explanation for this.

Looking at the circuits for some time, I started thinking how cool will it be to build a realistic mechanical analogy of the fourth order electrical system - pendulums could be ''LC circuits'', and a spring or elastic band between them for some weak mechanical coupling.

One pendulum would need to be self oscillating, which was the hard part.

I started thinking how cool would it be to actually use royer circuit to somehow drive the pendulum.. and idea came.
I had a theory that pendulum linked to a DC motor over some reduction will behave just like a low frequency parallel LC circuit... and indeed it did! I used lego motor with reduction and some pendulums made out of lego parts.

After some tweaking, I got the mock circuit to work. Chokes were replaced with 7805 current sources for this application.
I had a little overshoot in amplitude, but it was fixed with some resistance in series with motor.

Then I could proceed to coupling two pendulums together, and with some effort I observed both in and out of phase modes of operation!

I couldn't observe any of mode jumping, though, I saw in the electronic circuit.

My question is, is that possible at all? I would really appreciate if someone could shed light onto the phenomenon.

I had problems with my coupling - I'd really need some long flappy spring instead of rubber band which is too rough.
Still if all the interesting effects can really be observed I might go to building everything more properly than this!

Some other pictures I took.

rp181

Thu Oct 23 2008, 12:52AM

Registered Member #1062 Joined: Tue Oct 16 2007, 02:01AM
Location:
Posts: 1529

ahh...lego....
ile see if i can make one (even though i ruined the RCX in an attempt to mod it.... but i have NXT)

ShawnLG

Thu Oct 23 2008, 05:21AM

Registered Member #286 Joined: Mon Mar 06 2006, 04:52AM
Location:
Posts: 399

I have done some coupled pendulum experiments a year ago. I had use NIB magnets attached to the end of two strings. The magnetic field from the magnets provided the coupling between the two pendulums.

With the weak coupling and the very high Q of the system. I never had the pendulums lock together.

WaveRider

Thu Oct 23 2008, 12:20PM

Registered Member #29 Joined: Fri Feb 03 2006, 09:00AM
Location: Hasselt, Belgium
Posts: 500

Congrats Marko! You have just (re)discovered the phenomena of mode-coupling!

Those who design microwave or acoustic filters use this phenomena to great advantage... If you make an array of these resonant "rings" you can build a "negative refractive index" metamaterial....VERY sexy to optical guys at the moment... (but known to microwave engineers since the 1940s)...

Marko

Thu Oct 23 2008, 01:35PM

Registered Member #89 Joined: Thu Feb 09 2006, 02:40PM
Location: Zadar, Croatia
Posts: 3145

Hello guys, thanks for replies...

WaveRider wrote ...

Congrats Marko! You have just (re)discovered the phenomena of mode-coupling!

Any more information than that?

What should I look for.

I still don't understand the hysteretic 'mode locking/hopping thing. Does that have to do anything with phenomena like mode locking in lasers?

My mechanical analog so far failed to demonstrate it due to limited capabilities, but for electrical circuit, what is it related to?
What 'memorizes' the required bit of information?

Also, what are basic differences between the two normal modes I observed, apart from the phase shift and slightly lower amplitude in 180' mode. If I started building an approximation waveguide out of ''resonant rings'', what will I see? (I'm kinda out of capacitors now).

Marko

Coronafix

Thu Oct 23 2008, 11:54PM

Registered Member #160 Joined: Mon Feb 13 2006, 02:07AM
Location: Melbourne, Australia
Posts: 938

Not that i know anything about this, but is a standing wave being created and reflection from the receiver
creating the 180 shift? It would seem that it would need reflection to create the 180 shift, and therefore it's not
a case of 'memory', but of mirroring and getting locked onto the 'image' of itself in the receiver.
Just my thoughts on it, could be far off.

Steve Conner

Fri Oct 24 2008, 09:41AM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

Hey Marko, nice thread

As for what memorizes the 1 bit of information, consider this: A two transistor flip-flop (aka "bistable multivibrator") can remember 1 bit of information. Yet none of the components it's made from is capable of memorizing anything by itself.

(Of course for my argument I have to ignore the kind of crude write-only memory, all too familiar to 4hv members, where the component is functioning for "1" and blown to pieces for "0".)

So where is the memory of a flip-flop, if it's not in any of the components? If you can answer this, you can answer your own question, since your circuit is just another kind of bistable.

I won't answer my question yet: I'll leave it open here for discussion. Hint: non-linearity.

Coronafix

Tue Oct 28 2008, 10:45PM

Registered Member #160 Joined: Mon Feb 13 2006, 02:07AM
Location: Melbourne, Australia
Posts: 938

Steve, anymore information on this?
Marko, what are you using to drive the transmitter? Can you supply some info on your setup?
I have been thinking about this for a week now and no closer to understanding it, I would like to
reproduce your experiment. Are you able to supply a schematic? Thanks.

Danielle

Tue Oct 28 2008, 11:12PM

Registered Member #632 Joined: Mon Apr 09 2007, 01:09AM
Location:
Posts: 267

just a long shot guess on the transmitter....it looks like he may be using a simple ZVS driver, with just the tuned loop and inductors.

also, can you check with a spectrum analyzer if there is more distortion in the waves when you are operating 180 deg out of phase.

Steve Ward

Fri Oct 31 2008, 03:44AM

Registered Member #146 Joined: Sun Feb 12 2006, 04:21AM
Location: Austin Tx
Posts: 1055

By some tuning, I could get the system to the edge of in-phase mode, and then by slight lowering the coupling make it ''jump out'' of it into 180 deg. shift - with hysteresis! No matter how much coupling is increased again, I couldn't get the first mode back unless I cycle the power or re-tune!
I didn't have an explanation for this.

My guess is that the system moved into a more stable state, kind of like a ball at the top of a hill, but the top of the hill has a little hole that the ball sits in. You just knocked the ball off the hill and cant get it back up there. Now as to why the ball starts there to begin with???

I havent though about coupled systems in awhile, seems like a good brain teaser for when things are slow at work.

For anyone who knows controls (or math): can these systems be solved for with a state space model or something like that? Or would your model have to throw away the behavior Marko mentioned before (the non-linearity). Im only familiar with linearizing your model to get rid of these phenomena, but id like to understand it better!

Neato indeed.

I did a quick test just now on a smaller DRSSTC measuring both primary and secondary (Base) currents. With the primary tuned really low, and no real visible beating in the current envelope, the phase stays locked (at 0* i believe, not 180*). Tuning the primary a bit higher so beating is apparent shows a slight phase drift on the secondary from being locked with the primary, its clear to see the energy transfer as the secondary current peaks when the primary current drops off. Tuning the primary even higher leads to a 180* phase shift, almost no sparks, and very high primary currents... seems the system really doesnt like that at all. What im curious about now is, how would the phasing look if i took feedback from the secondary side? I find it funny that i dont really know the answer to this after years of playing with these things. My mediocre controls knowledge fails me... well because this is not a typical control problem.

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