%Exercise for Section 4.4, number 16
% y'' + 3*x' + 2*x=0
% with solution y(t)=-3*exp(-t) + 2*exp(-2*t), 
% y(t)=the position of the mass, 
% starting from 
% initial position y(0)=-1,
% with initial velocity y'(0)=-1.
% The damping constant is c=3/1=1.5, 
% the natural frequency omega0=sqrt(2).
% The constants depending on the initial conditions
c1=-3;c2=2;

t = linspace(0,15,150);
y = -3*exp(-t) + 2*exp(-2*t) ;

figure(1)
hold all
plot(t,y,'-r')
legend('y(t)')
title('Ex. 4.4.16: Overdamped harmonic motion c=1.5>sqrt(2)=\omega_0')
