From: "JACK L. URETSKY (C) 1996; HEP DIV., ARGONNE NATIONAL LAB, ARGONNE, IL 60439" <JLU@hep.anl.gov>
Date: Tue, 19 Nov 1996 13:53:59 -0600 (CST)
Hi all-
Jim Green asks:
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Consider an iron slinky-like spring which is stretched (magically)
horizontally and a copper guide-wire stretched horizontally and tautly just
above the slinky such that a magnet can be driven along the copper wire at
velocity, V. If the natural propagation velocity of motion in the slinky is
v, how do I analyze the resultant motion of the slinky? Assume v < V and
then v > V -- I take it that V = v is trivial, but who am I?
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Slinkies have too many degrees of freedom to discuss. The first
issue is what aspect of your problem to idealize.
Can we do it in terms of a vibrating string that is stretched
along the z direction and can vibrate freely in the x direction? Now
you are free to impose initial conditions on the string. At t=0 you may
have the string take any shape you like (but let's keep the problem
linear). If, as you suggest, you want conditions that vary with time,
then you will have a mixture of "initial conditions" (set along a
"spacelike" line") and a forcing function that constrains the shape
of the string in some way. The wave velocity on the string defines
a "light cone", outside of which you may impose arbitrary shapes on the
string.
Sorry for the mixed bag of analogies, but I have faith that
you can follow the gist.
Can you use the string to refine your question?
Regards,
Jack