% preliminary root search for cable with end masses and end springs

% delclare the beam dimensions and properties
L = 100;            % cable length in meters
A = 0.001;          % cable cross section area m^2
rho = 3*2700*A;     % cable mass per unit length in kg/m
mass_cable = rho*L; % total cable mass
T = 5000;           % cable tension in Newton
%
% Account for the tip mass;
%
mu_L = 100;  % the ratio of the concentrated tip mass at x=0 to mass_cable
mu_0 = 200;  % the ratio of the concentrated tip mass at x=L to mass_cable
k_0 = 100; % left-end stiffness relative to tension T;
k_L = 400; % right-end stiffness relative to tension T;

value_det = zeros(1,0);
betaL= zeros(1,0);
%search from beta l =0 to 30;

for x =0:0.1:30,
	
sx = sin(x); cx = cos(x); tx = tan(x);

det = (k_0^2 - mu_0*x^2)*(k_L^2 - mu_L*x^2)*sin(x);
det = det + ((k_0^2 - mu_0*x^2) +(k_L^2 - mu_L*x^2))*x*cos(x);
det = det-x^2*sin(x);

value_det=[value_det det];
betaL =[betaL x];

end;

figure(1);
plot(betaL, value_det);
xlabel('beta*L');
ylabel('Caracteristics roots ');
%legend(['frequency in Hertz = ', num2str(freq),' spring k = ', num2str(k), ' beta*L = ', num2str(beta_1)]);
title('Search for initial root locations');
axis([0 15 -10 10]);
grid on