% computes frequencies for 1 and 2 beads
% Sean Hardesty (16 Feb 2006)
% Adapted from Dr. Embree's bead3a.m

m = 0.125; % oz
sigma = 3.04*1.5; % lb/mv*mv

ell0 = 24.5; % cm
ell1 = 28; % cm
ell2 = 27; % cm

a1 = sigma*(1/ell0+1/ell1);
a2 = sigma*(1/ell1+1/ell2);
b1 = sigma/(ell1);

C = m*eye(2);
A = [ a1 -b1; 
    -b1  a2 ]; 

scale = 15690.64; %s^-2

B = scale*inv(C)*A;

fprintf('\n***************\n')
fprintf('With two beads:\n')
fprintf('***************\n')

[V,D] = eig(B);
rho = sqrt(diag(D));
freq = rho/(2*pi);
fprintf('Predicted natural frequencies:\n')
disp(freq)

measfreq=[23.8 40.7];
fprintf('Measured natural frequencies:\n')
disp(measfreq)

fprintf('\n***************\n')
fprintf('With one bead:\n')
fprintf('***************\n')

fprintf('Predicted natural frequency:\n')
disp(sqrt(scale*sigma/m*(1/ell0+1/(ell1+ell2)))/(2*pi))

fprintf('Measured natural frequency:\n')
disp([29.2])