1
GATE ECE 2014 Set 1
+2
-0.6
A system is described by the following differential equation, where u(t) is the input to the system and y(t) is output of the system $$\mathop y\limits^ \bullet \left( t \right) + 5y\left( t \right) = u\left( t \right)$$

When y(0) = 1 and u(t) is a unit step function, y(t) is

A
0.2+0.8e-5t
B
0.2-0.2e-5t
C
0.8+0.2e-5t
D
0.8-0.8e-5t
2
GATE ECE 2013
+2
-0.6
A system is described by the differential equation $${{{d^2}y} \over {d{t^2}}} + 5{{dy} \over {dt}} + 6y\left( t \right) = x\left( t \right)$$$Let x(t) be a rectangular pulse given by $$x\left( t \right) = \left\{ {\matrix{ {1\,\,\,\,\,\,\,\,\,0 \le \,t\, \le 2} \cr {0\,\,\,\,\,otherwise} \cr } } \right.$$$

Assuming that y(0) = 0 $${{dy} \over {dt}} = 0$$ at t = 0, the Laplace transform of y(t) is

A
$${{{e^{ - 2s}}} \over {s\left( {s + 2} \right)\left( {s + 3} \right)}}$$
B
$${{1 - {e^{ - 2s}}} \over {s\left( {s + 2} \right)\left( {s + 3} \right)}}$$
C
$${{{e^{ - 2s}}} \over {\left( {s + 2} \right)\left( {s + 3} \right)}}$$
D
$${{1 - {e^{ - 2s}}} \over {\left( {s + 2} \right)\left( {s + 3} \right)}}$$
3
GATE ECE 2011
+2
-0.6
If $$F\left( s \right) = L\left[ {f\left( t \right)} \right] = {{2\left( {s + 1} \right)} \over {{s^2} + 4s + 7}}$$ then the initial and final values of f(t) are respectively
A
0, 2
B
2, 0
C
0, 2/7
D
2/7, 0
4
GATE ECE 2010
+2
-0.6
Given f(t) = $${L^{ - 1}}\left[ {{{3s + 1} \over {{s^3} + 4{s^2} + \left( {K - 3} \right)s}}} \right].$$ If $$\matrix{ {Lim\,f\,\left( t \right) = 1,} \cr {t \to \infty } \cr } \,\,$$ then the value of K is
A
1
B
2
C
3
D
4
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