106 b Gs 2 s 1 a Gs6 2s 2 5s 2 5e d Gs 100s2 s 3 ss2 5s

106 )(b) G)s +2 s + 1 (a) Gs)+6) +2s + 2) 5(s + 2) 5e (d) G(s)= 100(s2 +s + 3) s(s2 + 5s + 3) s(s2 + 5s + 3) (e) G(s) = (f) G(s) 2-10. Find the inverse Laplace transforms of the functions in Problem 2-9

Solution

a) syms t s
f = (10*(s+1))/((s^2)+(s+4)+(s+6));
ilaplace(f)

Ans - 10*cos(3*t)*exp(-t)

d) syms t s
f = (5*exp(-2*s))/((s+1)*((s^2)+s+1));
ilaplace(f)

Ans - 5*heaviside(t - 2)*(exp(2 - t) - exp(1 - t/2)*(cos((3^(1/2)*(t - 2))/2) - (3^(1/2)*sin((3^(1/2)*(t - 2))/2))/3))