File:Drum vibration mode13.gif

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Drum_vibration_mode13.gif(250 × 130 pixels, file size: 137 KB, MIME type: image/gif, looped, 19 frames, 1.9 s)

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Description Illustration of vibrations of a drum.
Date (UTC)
Source self-made with MATLAB
Author Oleg Alexandrov
Other versions

Derivative works of this file:

 
This diagram was created with MATLAB.
Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Source code (MATLAB)

function main()

   k = 1; % k-th asimuthal number and bessel function
   p = 3; % p-th bessel root

   q=find_pth_bessel_root(k, p); 

   N=20; % used for plotting

   % Get a grid
   R1=linspace(0.0, 1.0, N); 
   Theta1=linspace(0.0, 2*pi, N);
   [R, Theta]=meshgrid(R1, Theta1);
   X=R.*cos(Theta);
   Y=R.*sin(Theta);

   T=linspace(0.0, 2*pi/q, N); T=T(1:(N-1));

   for iter=1:length(T);
      
      t = T(iter);
      Z=sin(q*t)*besselj(k, q*R).*cos(k*Theta);

      figure(1); clf; 
      surf(X, Y, Z);
      caxis([-1, 1]);
      shading faceted;
      colormap autumn;

      % viewing angle
      view(108, 42);
      
      axis([-1, 1, -1, 1, -1, 1]);
      axis off;

      file=sprintf('Frame_mode%d%d_%d.png', k, p, 1000+iter);
      disp(sprintf('Saving to %s', file));
      print('-dpng',  '-zbuffer',  '-r100', file);

      pause(0.1);
   end

% converted to gif with the command 
% convert -antialias -loop 10000 -delay 10  -scale 50% Frame_mode13* Drum_vibration_mode13.gif
 
   

function r = find_pth_bessel_root(k, p)

   % a dummy way of finding the root, just get a small interval where the root is
   
   X=0.5:0.5:(10*p+1); Y = besselj(k, X);
   [a, b] = find_nthroot(X, Y, p);

   X=a:0.01:b; Y = besselj(k, X);
   [a, b] = find_nthroot(X, Y, 1);

   X=a:0.0001:b; Y = besselj(k, X);
   [a, b] = find_nthroot(X, Y, 1);

   r=(a+b)/2;
   
function [a, b] = find_nthroot(X, Y, n)

   l=0;

   m=length(X);
   for i=1:(m-1)
      if ( Y(i) >= 0  & Y(i+1) <= 0 ) | ( Y(i) <= 0  & Y(i+1) >= 0 )
	 l=l+1;
      end

      if l==n
	 a=X(i); b=X(i+1);

	 %disp(sprintf('Error in finding the root %0.9g', b-a));
	 return;
      end
   end

   disp('Root not found!');

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8 June 2008

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Date/TimeThumbnailDimensionsUserComment
current23:00, 8 June 2008Thumbnail for version as of 23:00, 8 June 2008250 × 130 (137 KB)wikimediacommons>Oleg Alexandrov{{Information |Description={{en|1=x}} |Source=Own work by uploader |Author=Oleg Alexandrov |Date=x |Permission=x |other_versions=x }} x {{ImageUpload|full}}

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