% Illustration of a damped spring  function main()  % colors    black =    [0, 0, 0];    white    = 0.99*[1, 1, 1];    cobalt   = [0 	71 	171]/256;    pblue    = [0 	49 	83]/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    lw=2;    fs=20;     ww = 0.5;  % wall width    ms = 0.25; % the size of the mass            sw=0.1;    % spring width    curls = 8;     A = 0.45; % 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 = 4; % number of oscillations    damping = 0.1; % controls the damping    for i = 1:(N*No+5)        % 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*exp(-damping*t)*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*exp(-damping*3*pi/2)-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              pause(0.1);           end  % The following command was used to create the animated figure.     % convert -antialias -loop 10000  -delay 7 -compress LZW Spring_frame10* Damped_spring.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    theta=pi/6;    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);    Y=-sw*cos(XX);    Z=sw*sin(XX);     %  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)];    N=length(X);    for i=1:N;       V=M*[X(i), Z(i)]';       X(i)=V(1); Z(i)=V(2);    end  %  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)];     N=length(X);    for i=1:N;       V=M*[X(i), Y(i)]'+A';       X(i)=V(1); Y(i)=V(2);    end  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);     V=l*(0:0.1:1);     for i=0:(no-1)       plot(S+ i*spacing + V, V, 'color', wall_color)    end