Date: Fri, 15 Oct 2004 16:50:59 -0500

Author: A Gavrin

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

Post:

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Here's a possible wrinkle. If the pendula can go all the way over, you
can end up with a full twist stored in the spring between two pendula
that "look" parallel. This would be a "kink" type solution similar to
those observed in some systems that have soliton solutions, e.g., the
"sine-gordon" equation.

Did they show that, Sam?

- Andy



sampere wrote:

> And a followup, this effect wasn't discovered until the late '80s, so
> it's relatively new.
>
> 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
>>***********************************************************************
>>
>>

--
Dr. Andrew D. Gavrin
Department of Physics, 402 N. Blackford St.
Indiana Univ.-Purdue Univ. Indianapolis
Indianapolis, IN 46202-3273

317-274-6909 (Ph) -2393 (FAX)
agavrin@iupui.edu


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Here's a possible wrinkle. If the pendula can go all the way over, you
can end up with a full twist stored in the spring between two pendula
that "look" parallel. This would be a "kink" type solution similar to
those observed in some systems that have soliton solutions, e.g., the
"sine-gordon" equation.



Did they show that, Sam?



- Andy







sampere wrote:

And a followup, this effect wasn't discovered until the late '80s, so
it's relatively new.



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  
 href="mailto:reberg@physics.umd.edu">reberg@physics.umd.edu


 href="http://www.physics.umd.edu/lecdem">www.physics.umd.edu/lecdem

***********************************************************************

  

-- 

Dr. Andrew D. Gavrin

Department of Physics, 402 N. Blackford St.

Indiana Univ.-Purdue Univ. Indianapolis

Indianapolis, IN 46202-3273



317-274-6909 (Ph)   -2393 (FAX)

agavrin@iupui.edu