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Re: [GraphingCalcUsers] twisty rod and fourier series

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  • Arne Landsberg
    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

      ----------
      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
    • Chris Young
      ... 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?
      • C Goodman-Strauss
        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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