1
GATE ECE 1997
+1
-0.3
The Laplace Transform of eat .cos$$\left( {\alpha t} \right).u\left( t \right)$$ is equal to
A
$${{\left( {s - \alpha } \right)} \over {{{\left( {s - \alpha } \right)}^2} + {\alpha ^2}}}$$
B
$${{\left( {s + \alpha } \right)} \over {{{\left( {s + \alpha } \right)}^2} + {\alpha ^2}}}$$
C
$${1 \over {{{\left( {s - \alpha } \right)}^2}}}$$
D
none of the above
2
GATE ECE 1995
+1
-0.3
The final value theorem is used to find the
A
steady state value of the system output
B
initial value of the system output
C
transient behavior of the system output
D
none of these
3
GATE ECE 1995
+1
-0.3
If L$$\left[ {f\left( t \right)} \right]$$ = $${{2\left( {s + 1} \right)} \over {{s^2} + 2s + 5}}$$, then $$f\left( {0 + } \right)\,$$ and $$f\left( \infty \right)$$ are given by
A
0, 2 respectively
B
2, 0 respectively
C
0, 1 respectively
D
2/5, 0 respectively
4
GATE ECE 1994
+1
-0.3
The laplace transform of a unit ramp function starting at t=a, is
A
$${1 \over {{{\left( {s + a} \right)}^2}}}$$
B
$${{{e^{ - as}}} \over {{{\left( {s + a} \right)}^2}}}$$
C
$${{{e^{ - as}}} \over {{s^2}}}\,$$
D
$${a \over {{s^2}}}$$
EXAM MAP
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