echo on
% This script will plot a series of functions of the 
% form c1*exp(lam1*t) + c2*exp(lam2*t) + ... c10*exp(lam10*t)
% where c1 to c10 are randomly chosen between -2.5 and 2.5
% and lam1 to lam10 are complex roots whos real parts are 
% randomly chosen between -2 and 0, and the imaginary parts are
% chosen between 1 and 4.  
% The plot will be displayed until a key is struck on the 
% keyboard.   

t = [0:.1:10];   % Define Time Axis for function evaluation

% Loop through 10 different functions 

for k=1:10
  cr = 5*(rand(1,5) - .5);     %  Randomly pick 5 complex coefficients
  ci = 5*(rand(1,5) - .5);
  c = [(cr+j*ci), (cr-j*ci)]; 
  subplot(3,1,1), plot(abs(c))      %   Plot out magnitudes
  ylabel('Coefficent Magnitudes')     
  lamr = -2*rand(1,5);         %  Randomly pick 10 complex frequenies
  lami = 1 + 3*rand(1,5);
  lam = [(lamr+j*lami), (lamr-j*lami)];
  subplot(3,1,2), plot(abs(lam))    %   Plot out magnitudes 
  ylabel('Time Constant Magnitudes')
  subplot(3,1,3), plot(t, real(c*exp(lam'*t)))  %  Evaluate and plot function
  ylabel('Function')
  xlabel('seconds')
  pause                        %  Hold figure until Key is struck
end

echo off