clc

close all

clear

syms s t

num = s+3;

den = s^2+2*s+5;

Fs = num/den

res = solve(den)

Ft = simplify(ilaplace(Fs, s, t))

ts = 0:0.01:10;

Ft = subs(Ft, t, ts);

plot(ts, Ft, 'LineWidth', 2);

hold on;

plot(ts, sqrt(2)*exp(-ts), '-.r', ts, -sqrt(2)*exp(-ts), '-.r', 'LineWidth', 1)

grid on;