warning off
pkg load symbolic
syms t

k = 26520;
m = 450;
c = 1000;
x0 = 0.54;
v0 = 1;
wn = sqrt(k/m)
# Sistema subamortecido
fa = c/(2*sqrt(k*m))
wd = wn*sqrt(1-fa^2)
C1l = x0;
C2l = (v0+fa*wn*x0)/wd;
x1 = (e^(-fa*wn*t))*(C1l*cos(wd*t)+C2l*sin(wd*t))
figure 1
ezplot(x1,[0 5])
# Sistema criticamente amortecido
c = 2*sqrt(k*m)
C1 = x0;
C2 = v0+wn*x0;
x2 = (C1+C2*t)*e^(-wn*t)
figure 2
ezplot(x2,[0 5])
# Sistema Superamortecido
c = 10000;
fa = c/(2*sqrt(k*m))
C1 = (x0*wn*(fa+sqrt(fa^2-1))+v0)/(2*wn*sqrt(fa^2-1))
C2 = (-x0*wn*(fa-sqrt(fa^2-1))-v0)/(2*wn*sqrt(fa^2-1))
x3 = C1*e^((-fa+sqrt(fa^2-1))*wn*t)+C2*e^((-fa-sqrt(fa^2-1))*wn*t)
figure 3
ezplot(x3,[0 5])