## Re: [GraphingCalcUsers] twisty rod and fourier series

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• On Jul 31, 2006, at 7:10 PM, C Goodman-Strauss wrote: Hello, in the Advanced Applied class I m teaching (aka A First Look at Fourier Series Stuff), we are
Message 1 of 6 , Aug 1, 2006
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On Jul 31, 2006, at 7:10 PM, C Goodman-Strauss wrote:
Hello, in the Advanced Applied class I'm teaching (aka A First Look at
Fourier Series Stuff), we are going over solving various physically
motivated boundary value problems. A problem came up today, describing
the motion of a rod fixed at one end, given a vigorous twist and
released. The solution seemed a little weird looking, so I made a GC
file to take a look. I dunno, does this look realistic?
Have fun,
Chaim

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No!
At first glance it didn't seem right
Then looking closer I expected the twist to start at the moving end and
travel downward to the fixed end

So I would say it looks OK with n
going 0 to 1, 2 to 3, 4 to 3, and 2 to 1

But to me it doesn't look right with n
going 1 to 2, 3 to 4, 3 to 2, and 1 to 0

a good distraction to my busy day
Arne
• ... This looks great!! It certainly looks plausible. There are interesting little sub-twists going on within the twists. This brings up the whole fascinating
Message 2 of 6 , Aug 1, 2006
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On Jul 31, 2006, at 10:10 PM, C Goodman-Strauss wrote:

>
> Hello, in the Advanced Applied class I'm teaching (aka A First Look at
> Fourier Series Stuff), we are going over solving various physically
> motivated boundary value problems. A problem came up today, describing
> the motion of a rod fixed at one end, given a vigorous twist and
> released. The solution seemed a little weird looking, so I made a GC
> file to take a look. I dunno, does this look realistic?
• Here s a fun variation on the twisty rod file: Simply plot z=A(x,y); this shows, at x,y, the amount twisted at position x along the rod, at time y. However,
Message 3 of 6 , Aug 2, 2006
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Here's a fun variation on the twisty rod file: Simply plot z=A(x,y);
this shows, at x,y, the amount twisted at position x along the rod, at
time y. However, really, for the rod, 0<x<1 and y>0 (shown in red). If
we look at a larger domain, we see that the series sums up to an
egg-carton shape, with square pyramids, up and down, for the dimples.
(Alternatively, this could be seen as the top of a layer of packed
rhombic dodecahedra)

As far as I can tell, the edges are actually sharp, at least as the
number N of terms increases. (Even around n=10 or so, they would appear
perfectly sharp, I think, if rendered exactly, but GC is assembling the
picture out of little squares)
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