File:Simple harmonic oscillator.gif

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Simple_harmonic_oscillator.gif(116 × 359 pixels, file size: 52 KB, MIME type: image/gif, looped, 15 frames, 1.1 s)

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Illustration of a en:Simple harmonic oscillator

Source self-made with en:Matlab. Converted to gif animation with the en:ImageMagick convert tool (see the specific command later in the code).
Author Oleg Alexandrov
Other versions

Damped spring.gifDamped spring.gif Damped version

GIF development
Matlab Logo.png
This diagram was created with MATLAB.


function main()

% colors
   red      = [0.867    0.06    0.14];
   blue     = [0        129     205]/256;
   green    = [0        200     70]/256;
   black    = [0        0       0];
   white    = [1        1       1]*0.99;
   cardinal = [196      30      58]/256;
   cerulean = [0        123     167]/256;
   denim    = [21       96      189]/256;
   cobalt   = [0        71      171]/256;
   pblue    = [0        49      83]/256;
   teracotta= [226      114     91]/256;
   tene     = [205      87      0]/256;
   wall_color   = pblue;
   spring_color = cobalt;
   mass_color   = tene;
   a=0.65; bmass_color   = a*mass_color+(1-a)*black;
   % linewidth and fontsize

   ww = 0.5;  % wall width
   ms = 0.25; % the size of the mass        
   sw=0.1;    % spring width
   curls = 8;

   A = 0.2; % the amplitude of spring oscillations
   B = -1; % the y coordinate of the base state (the origin is higher, at the wall)

   %  Each of the small lines has length l
   l = 0.05;

   N = 15;  % times per oscillation 
   No = 1; % number of oscillations
   for i = 1:N*No

      % set up the plotting window
      figure(1); clf; hold on; axis equal; axis off;

      t = 2*pi*(i-1)/(N-0)+pi/2; % current time
      H= A*sin(t) +  B;      % position of the mass

      % plot the spring from Start to End
      Start = [0, 0]; End = [0, H];
      [X, Y]=do_plot_spring(Start, End, curls, sw);
      plot(X, Y, 'linewidth', lw, 'color', spring_color); 

      % Here we cheat. We modify the point B so that the mass is attached exactly at the end of the
      % spring. This should not be necessary. I am too lazy to to the exact calculation.
      K = length(X); End(1) = X(K); End(2) = Y(K);
      % plot the wall from which the spring is hanging
      plot_wall(-ww/2, ww/2, l, lw, wall_color);

      % plot the mass at the end of the spring
      X=[-ms/2 ms/2 ms/2 -ms/2 -ms/2 ms/2]+End(1); Y=[0 0 -ms -ms 0 0]+End(2);
      H=fill(X, Y, mass_color, 'EdgeColor', bmass_color, 'linewidth', lw);

          % the bounding box
          Sx = -0.4*ww;  Sy = B-A-ms+0.05;
          Lx = 0.4*ww+l; Ly=l;
          axis([Sx, Lx, Sy, Ly]);
          plot(Sx, Sy, '*', 'color', white); % a hack to avoid a saveas to eps bug
      saveas(gcf, sprintf('Spring_frame%d.eps', 1000+i), 'psc2') %save the current frame
      disp(sprintf('Spring_frame%d', 1000+i)); %show the frame number we are at

% The following command was used to create the animated figure.    
% convert -antialias -loop 10000  -delay 7 -compress LZW Spring_frame10* Simple_harmonic_oscillator.gif

function [X, Y]=do_plot_spring(A, B, curls, sw);
%  plot a 3D spring, then project it onto 2D. theta controls the angle of projection.
%  The string starts at A and ends at B

   % will rotate by theta when projecting from 1D to 2D
   Npoints = 500;
   % spring length
   D = sqrt((A(1)-B(1))^2+(A(2)-B(2))^2);
   X=linspace(0, 1, Npoints);

   XX = linspace(-pi/2, 2*pi*curls+pi/2, Npoints);
%  b gives the length of the small straight segments at the ends
%  of the spring (to which the wall and the mass are attached)
   b= 0.05; 

% stretch the spring in X to make it of length D - 2*b
   N = length(X);
   X = (D-2*b)*(X-X(1))/(X(N)-X(1));
% shift by b to the right and add the two small segments of length b
   X=[0, X+b X(N)+2*b]; Y=[Y(1) Y Y(N)]; Z=[Z(1) Z Z(N)]; 

   % project the 3D spring to 2D
   M=[cos(theta) sin(theta); -sin(theta) cos(theta)];
   for i=1:N;
      V=M*[X(i), Z(i)]';
      X(i)=V(1); Z(i)=V(2);

%  shift the spring to start from 0
   X = X-X(1);
% now that we have the horisontal spring (X, Y) of length D,
% rotate and translate it to go from A to B
   Theta = atan2(B(2)-A(2), B(1)-A(1));
   M=[cos(Theta) -sin(Theta); sin(Theta) cos(Theta)];

   for i=1:N;
      V=M*[X(i), Y(i)]'+A';
      X(i)=V(1); Y(i)=V(2);

function plot_wall(S, E, l, lw, wall_color)

%  Plot a wall from S to E.
   no=20; spacing=(E-S)/(no-1);
   plot([S, E], [0, 0], 'linewidth', 1.8*lw, 'color', wall_color);


   for i=0:(no-1)
      plot(S+ i*spacing + V, V, 'color', wall_color)

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.

Annotations This image is annotated: View the annotations at Commons

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current03:12, 24 June 2007Thumbnail for version as of 03:12, 24 June 2007116 × 359 (52 KB)Oleg Alexandrov (talk | contribs)tweak
03:10, 24 June 2007Thumbnail for version as of 03:10, 24 June 2007157 × 362 (51 KB)Oleg Alexandrov (talk | contribs)Reverted to earlier revision
03:10, 24 June 2007Thumbnail for version as of 03:10, 24 June 2007116 × 359 (7 KB)Oleg Alexandrov (talk | contribs)tweak
02:42, 24 June 2007Thumbnail for version as of 02:42, 24 June 2007157 × 362 (51 KB)Oleg Alexandrov (talk | contribs){{Information |Description= |Source=self-made with en:Matlab. Converted to gif animation with the en:ImageMagik convert tool. |Date= ~~~~~ |Author= Oleg Alexandrov }} {{PD-self}}
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