Question

Find out inverse Laplace transforms of the following provided the

systems assuming a) system is stable, b) assuming system is causal.

2

H(s) -

(5-1)(3-3)

1

H(s) -

(s + 1)(3+3)

1

H(s) =

(s + 1)(-3)

Answer 1

Given:

$r(t) ∗ h(t) = b(t)$

$\implies R(s)H(s) = B(s)$

$R(s) =\frac{1}{s^2}$

$B(s) = \frac{s}{s^2+5s+6}$

$\implies H(s) =\frac{s^3}{s^2+5 s+6}$

$Y (s) = U(s)X(s)$

$\implies Y (s) =\frac{s^2}{s^2+5 s+6}$

Taking Inverse Laplace Transform

$\implies y(t) = 4e^{−2t}u(t) − 9e^{−3t}u(t) + δ(t)$