Date: Fri, 15 Oct 2004 13:16:11 -0400

Author: sampere

Subject: Re: localized energy mode demo, i.e pendulum revisited

Post:

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I like Dick's answer below. This was a very cool demo and an
interesting problem. The hint is in the subject line - localized energy
mode.

For small starting amplitudes, everything is linear - especially the
pendulum. For large starting amplitudes, the pendulum is nonlinear.
After some time, most of the energy of the system is transferred into
one pendulum only - it swings with a very large amplitude. It was very
cool to watch this system transform from a bunch of identical
oscillators to what looked like chaotic motion, and finally into this
localized energy mode with only one swinging. This was stable for a
while. The analogy was very cool.

Imagine (well, everyone except for JZ) a rock dropped into a calm pond,
the water waves spread across the pond. In a nonlinear system, the
waves wouldn't spread, the water would whoosh out, then whoosh back, and
on and on. So particles even not so very far away would never know that
a rock was dropped.

Anyway, the talk was very interesting and given at a level so even my
feeble mind could understand the important points.

Enjoy the weekend y'all,

Sam

Richard Berg wrote:

>For small amplitudes, they might end up all moving back and forth together
>in phase.
>
>For large amplitudes, they might end up moving back and forth with
>adjacent pendula out of phase.
>
>But then again, they might not.
>
>DB
>
>On Fri, 15 Oct 2004, sampere wrote:
>
>
>
>>I saw the coolest demo yesterday. Al Sievers from Cornell gave a
>>colloquium here yesterday and brought a demo with him.
>>
>>Picture a dozen small identical pendulms suspended from a single rod,
>>perhaps from a bearing, so the rod does not play any role in
>>transferring energy. Then, connect each of the pivot points with
>>springs so that as the pendulums oscillate, the springs either wind up
>>or unwind. The direction of oscillation is perpendicular to the length
>>of the suspension rod, i.e., if the pendulums all dangle from rod
>>horizontal and parallel to your screen, the pendulums oscillate in and
>>out of the screen.
>>
>>So, here are two questions for you:
>>
>>1) For small starting amplitudes, the initial conditions for all pendula
>>being equal, what do expect to see?
>>2) Same as 1, but for very large starting amplitudes?
>>
>>I'll post the answer later after I hear your thoughts.
>>
>>Sam
>>
>>
>>
>>
>
>***********************************************************************
>Dr. Richard E. Berg, Professor of the Practice
>Director, Physics Lecture-Demonstration Facility
>U.S. mail address:
>Department of Physics
>University of Maryland
>College Park, MD 20742-4111
>Phone: (301) 405-5994
>FAX: (301) 314-9525
>e-mail reberg@physics.umd.edu
>www.physics.umd.edu/lecdem
>***********************************************************************
>
>

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I like Dick's answer below.  This was a very cool demo and an
interesting problem.  The hint is in the subject line - localized
energy mode.



For small starting amplitudes, everything is linear - especially the
pendulum.  For large starting amplitudes, the pendulum is nonlinear. 
After some time, most of the energy of the system is transferred into
one pendulum only - it swings with a very large amplitude.  It was very
cool to watch this system transform from a bunch of identical
oscillators to what looked like chaotic motion,  and finally into this
localized energy mode with only one swinging.  This was stable for a
while.  The analogy was very cool.



Imagine (well, everyone except for JZ) a rock dropped into a calm pond,
the water waves spread across the pond.  In a nonlinear system, the
waves wouldn't spread, the water would whoosh out, then whoosh back,
and on and on.  So particles even not so very far away would never know
that a rock was dropped.



Anyway, the talk was very interesting and given at a level so even my
feeble mind could understand the important points.



Enjoy the weekend y'all,



Sam



Richard Berg wrote:

cite="midPine.OSF.4.44.0410151217540.370-100000@student1.physics.umd.edu">
For small amplitudes, they might end up all moving back and forth together
in phase.

For large amplitudes, they might end up moving back and forth with
adjacent pendula out of phase.

But then again, they might not.

DB

On Fri, 15 Oct 2004, sampere wrote:



I saw the coolest demo yesterday.  Al Sievers from Cornell gave a
colloquium here yesterday and brought a demo with him.

Picture a dozen small identical pendulms suspended from a single rod,
perhaps from a bearing, so the rod does not play any role in
transferring energy. Then, connect each of the pivot points with
springs so that as the pendulums oscillate, the springs either wind up
or unwind. The direction of oscillation is perpendicular to the length
of the suspension rod, i.e., if the pendulums all dangle from rod
horizontal and parallel to your screen, the pendulums oscillate in and
out of the screen.

So, here are two questions for you:

1) For small starting amplitudes, the initial conditions for all pendula
being equal, what do expect to see?
2) Same as 1, but for very large starting amplitudes?

I'll post the answer later after I hear your thoughts.

Sam





***********************************************************************
Dr. Richard E. Berg, Professor of the Practice
Director, Physics Lecture-Demonstration Facility
U.S. mail address:
Department of Physics
University of Maryland
College Park, MD 20742-4111
Phone: (301) 405-5994
FAX: (301) 314-9525
e-mail reberg@physics.umd.edu
www.physics.umd.edu/lecdem
***********************************************************************





--------------050104030003060603050700--
From sampere@physics.syr.edu Fri Oct 15 10:05:38 2004

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