A linear time invariatiant system has an impulse response

Home » Signals and Systems » Signals and systems electrical engineering miscellaneous » Question

A linear time invariatiant system has an impulse response e^2t, t > 0. If the initial conditions are zero and the input is e^3t, the output for t > 0 is

1. e^3t – e^2t
2. e^5t
3. e^3t + e^2t
4. None of these

Correct Option: A

Output C(s) = H (s). R (s) =	1	.	1	=	(s - 2) - (s - 3)	then C (t) = L – 1 [C(s)]
	s - 2		s - 3		(s - 2)(s - 3)

= L^-1		1		- L^-1		1		= e^3t - e^2t
		(s - 3)				(s - 2)