If system is initially at rest, the response to a unit

If system is initially at rest, the response to a unit step u(t) is given by 1/2 (1 – e^{– 2t}) The response to a signal u(t) + 2δ (t) is given by

Here C(t) =	1	(1 - e^-2t, R(s) =	1
	2		s

i.e C(s) =	1		1	-	1		=	1
	2		s		s + 2			s(s + 2)

H(s) =	L(s)
	R(s)

u(s) =	1
	s + 2

Now for R'(s) =	1	+ 2
	s

⇒ C'(s) =

+ 2

2s + 1

(s + 2)

s(s + 2)

s + 2

1	+	3	e^-2t
2		2

1	+	1	e^-2t
2		2