1
GATE ECE 2016 Set 1
+2
-0.6
The Laplace transform of the casual periodic square wave of period T shown in the figure below is
A
$$F\left( s \right) = {1 \over {1 + {e^{ - sT/2}}}}$$
B
$$F\left( s \right) = {1 \over {s\left[ {1 + {e^{{{sT} \over 2}}}} \right]}}$$
C
$$F\left( s \right) = {1 \over {s\left( {1 + {e^{ - sT}}} \right)}}$$
D
$$F\left( s \right) = {1 \over {1 - {e^{ - sT}}}}$$
2
GATE ECE 2015 Set 2
Numerical
+2
-0
Let x(t) = a s(t) +s(-t) with s(t) = $$\beta {e^{ - 4t}}u\left( t \right)$$, where u(t) is unit step function. If the bilateral Laplace transform of x(t) is $$X\left( S \right)\, = {{16} \over {{S^2} - 16}} - 4 < {\mathop{\rm Re}\nolimits} \left\{ s \right\} < 4;$$\$

Then the value of β is ______.

3
GATE ECE 2015 Set 1
+2
-0.6
The solution of the differential equation $${{h\left( {t + 1} \right)} \over {h\left( t \right)}}\,\,\,\,\,{{{d^2}y} \over {d{t^{ \to 2}}}} + {{2\,dy} \over {dt}} + y\, = \,0$$ with $$\,y\left( 0 \right)\, = \,y'\left( 0 \right)\, = \,1$$ is
A
$$\left( {2 - t} \right){e^t}$$
B
$$\left( {1 + 2t} \right){e^{ - t}}$$
C
$$\left( {2 + t} \right){e^{ - t}}$$
D
$$\left( {1 - 2t} \right){e^t}$$
4
GATE ECE 2014 Set 4
+2
-0.6
The unilateral Laplace transform of F(t) is $${1 \over {{s^2} + s + 1}}$$. Which one of the following is the unilateral Laplace transform of g(t) = $$t \cdot f\left( t \right)$$
A
$${{ - s} \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$
B
$${{ - \left( {2s + 1} \right)} \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$
C
$${s \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$
D
$${{2s + 1} \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$
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