1
GATE ECE 2004
+2
-0.6
A system described by the differential equation: $${{{d^2}y} \over {d{t^2}}} + 3{{dy} \over {dt}} + 2y = x(t)$$ is initially at rest. For input x(t) = 2u(t), the output y(t) is
A
$$(1 - 2{e^{ - t}} + {e^{ - 2t}})\,u(t)$$
B
$$(1 + 2{e^{ - t}} - 2\,{e^{ - 2t}})\,u(t)$$
C
$$(0.5 + {e^{ - t}} + 1.5\,{e^{ - 2t}})\,u(t)$$
D
$$(0.5 + 2{e^{ - t}} + 2\,\,{e^{ - 2t}})\,u(t)$$
2
GATE ECE 2004
+2
-0.6
A rectangular pulse train s(t) as shown in Fig.1 is convolved with the signal $${\cos ^2}$$ ($$4\pi \,{10^{3\,}}$$t). The convolved signal will be a
A
DC
B
12 kHz sinusoid
C
8 kHz sinusoid
D
14 kHz sinusoid
3
GATE ECE 2004
+2
-0.6
A causal system having the transfer function H(s) = $${1 \over {s + 2}}$$, is excited with 10 u(t). The time at which the output reaches 99% of its steady state value is
A
2.7 sec
B
2.5 sec
C
2.3 sec
D
2.1 sec
4
GATE ECE 2001
+2
-0.6
The impulse response function of four linear system S1, S2, S3, S4 are given respectively by

$${h_1}$$(t), = 1;

$${h_2}$$(t), = U(t);

$${h_3}(t)\, = \,{{U(t)} \over {t + 1}}$$;

$${h_4}(t)\, = {e^{ - 3t}}U(t)$$ ,

where U (t) is the unit step function. Which of these system is time invariant, causal, and stable?

A
SI
B
S2
C
S3
D
S4
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