close all
clear all

gamma = 15.0;
omega = 0.1;

u_0 = [0; 1];

Dt = 0.001;

t_0 =0.0;
T   = 2.0;

tk = t_0:Dt:(t_0+T);

K = length(tk);

uk = zeros(2,K);


l1 = -gamma+sqrt(gamma^2-omega^2);
l2 = -gamma-sqrt(gamma^2-omega^2);
c1 = (u_0(2)-l2*u_0(1))/(l1-l2);
c2 = -(u_0(2)-l1*u_0(1))/(l1-l2);
x  = c1*exp(l1*tk)+c2*exp(l2*tk);

x1  = c1*exp(l1*tk);

x2  = c2*exp(l2*tk);


figure(1)
handle = axes
set(handle,'FontSize',18)
handle = plot(tk,x,'g-',tk,x1,'b--',tk,x2,'r:');
set(handle,'LineWidth',4);
axis([0 2 -0.05 0.05])
grid on
legend('c_1e^{\lambda_1 t}+c_2e^{\lambda_2 t}','c_1e^{\lambda_1 t}','c_2e^{\lambda_2 t}',4)


figure(2)
handle = axes
set(handle,'FontSize',18)
handle = plot(tk,x,'g-',tk,x1,'b--',tk,x2,'r:');
set(handle,'LineWidth',4);
axis([0 0.2 -0.05 0.05])
grid on
legend('c_1e^{\lambda_1 t}+c_2e^{\lambda_2 t}','c_1e^{\lambda_1 t}','c_2e^{\lambda_2 t}',4)