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Subject: "Complex Wave problem"     Previous Topic | Next Topic
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Conferences The CTK Exchange College math Topic #44
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Jan-05-01, 12:26 PM (EST)
Click to EMail sderamus Click to send private message to sderamus Click to add this user to your buddy list  
"Complex Wave problem"
   OK, this is a good one - inspired by my 5 yo daughter's jump rope that she just got from Santa. Assuming she (designated as MED) is standing at point (0,0,0) holding the rope and her friend (designated as LAK)is standing way down the x axis holding the other end of the rope, and there is no slack in the rope. MED waves her hand left and right along the y axis between -1 and 1 in simple harmonic motion. Thus she creates a sine wave traveling down the length of the rope. LAK simultaneously waves her end up and down along the z axis between 1 and -1. How can we come up with a formula that describes the position of any point of the rope at time T? I suspect we need to establish the length of the rope and we could arbitrarily pick 10, but I wondered if we had to assume that the movements were significantly small enough compared to the length of the rope to make the problem easier. If so, then let's make it 100. (I know, I know, no 5 year old could hold up such a rope, but this is a math problem, not an engineering one!!!)

I think it would make the problem simpler if reduced to cylindrical coordinates, and thus there are only three variables and not four (r, theta, and t verus x, y, z, and t). Remember that there is a boundary problem that complicates things since at both MED's end and LAK's end the rope can only travel in one direction. If that overly complicates things, then maybe we can work the problem from another angle.

As to my background - I have an undergraduate degree in math, but it is coming up on 20 years and I'm a bit rusty. I've been pulling out my old Diff Eq and Fourier Analysis books but man it's been way too long!!


Sterling L. DeRamus

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Jan-05-01, 01:00 PM (EST)
Click to EMail alexb Click to send private message to alexb Click to view user profileClick to add this user to your buddy list  
1. "RE: Complex Wave problem"
In response to message #0
   LAST EDITED ON Jan-05-01 AT 01:01 PM (EST)

Dear Sterling:

Assume I spend some time and write down you the solution, what are you going to do with it? Plot, just wonder at the expression?

I know a 75 year old person who has recently dusted his old books and began reading them - just to keep his gray matter active. The last I heard he was mastering a Complex Variables book. He does this as every one else - by reading and solving exercises and thinking about what he learned. If he had a question I would be happy to help him.

But my impression from your letter that sounds very enthusiastic is that you in fact do not care a little bit. Nah, I can't spent of my time on this. I would not mind if a visitor wanted to answer your question, but no, I do not have time to oblige every one's whim.

All the best,
Alexander Bogomolny

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