# Energy transfer in a coupled pendulum

If you take a look at this video you will see what kind of a coupled pendulum I'm talking about.

So I made a similar one in my high school's physics lab, using light metal bobs(much lighter than the Easter eggs he's used in the video) and thin copper wire.

My pendulum did work the same way, i.e. one would stop as the other would swing with max amplitude, which continues periodically without much damping. But the frequency of the combined periodic motion in my case was much slower than that in the video. His pendulum stops after a few oscillations while mine took 10-15 oscillations to completely transfer the energy(I think this is because I used a lighter weight)

My Question:

In the video the person swings one of the pendulums perpendicular to the wire. I tried swinging it parallel to the wire and nothing happened. The pendulum I initially provided energy to kept swinging with the same amplitude for a long time.
Why doesn't energy transfer take place when I swing the one of the pendulums parallel to the above wire? It should because the energy is being transferred by waves through the string. This motion should also produce waves.

Possible Reasons:

• Maybe the energy transfer takes a lot of time, hours perhaps? I hardly observed it for ten minutes.
• There's too much damping, although in which case the first pendulum should stop quickly too.
• The energy transfer is happening in a way not compatible with the direction the bob is swinging in.

I really can't seem to explain any of the above reasons. Maybe it's an entirely different reason altogether. Any help would be appreciated!

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The string that the eggs hang from is allowed to move in the same direction as the eggs when swung perpendicular. This is not the case when you swing in parallel. If you hold the top string still and swing the egg perpendicular you will see that almost none of that energy transfers to the other egg and the egg you pushed will continue to swing.

Basically the main string only has one degree of freedom and moving parallel is not the direction that the string moves.

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I never thought of that! I will try that out, holding the above string fixed. – udiboy1209 Jul 21 '13 at 7:18

It would be of interest to find the corresponding equations of motion, at least equations of motion that capture the observed phenomenon (yours and the one in the video). It is probably due to a too weak coupling stiffness in the parallel direction that you do not see much. What is in the video is potentially a purely nonlinear phenomenon called an internal resonance that arises only when very specific conditions on the mass and stiffness of the system of interest are met.

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Could you describe more about internal resonance, some links would help too. – udiboy1209 Jul 21 '13 at 7:15
I kind of don't believe "arises only when very specific conditions on the mass and stiffness of the system of interest are met". I tried various variations of the experiment, i.e. different string lengths, different masses, 3 pendulums, etc. In each case I found some periodic motion being followed, of course not the same in each case, but definitely periodic. – udiboy1209 Jul 21 '13 at 9:27
@udiboy I may be wrong on the internal resonance explanation but you may want to have a look at: ltas-vis.ulg.ac.be/cmsms/uploads/File/25_nld.pdf or books.google.ca/… or maybe link.springer.com/article/10.1007%2FBF01176546 – pluton Jul 21 '13 at 18:24