1
GATE IN 2012
+1
-0.3
The unilateral Laplace transform of $$f(t)$$ is
$$\,{1 \over {{s^2} + s + 1}}.$$ The unilateral Laplace transform of $$t$$ $$f(t)$$ is
A
$$- {s \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$
B
$$- {{2s + 1} \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$
C
$${s \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$
D
$${{2s + 1} \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$
2
GATE IN 2010
+1
-0.3
$$u(t)$$ represents the unit step function. The Laplace transform of $$u\left( {t - \tau } \right)$$ is
A
$${1 \over {s\tau }}$$
B
$${1 \over {s - \tau }}$$
C
$${{{e^{ - s\tau }}} \over s}$$
D
$${e^{ - s\tau }}$$
3
GATE IN 1995
Fill in the Blanks
+1
-0
The laplace transform of a function $$f(t)$$ is defined by
$$F\left( s \right) = L\left\{ {f\left( t \right)} \right\} = \int\limits_0^\infty {{e^{ - st}}f\left( t \right)dt.}$$.
Find the inverse laplace transform of $$F(s-a)$$
4
GATE IN 1995
Subjective
+1
-0
Find $$L\left\{ {{e^{at}}\,\cos \,\omega t} \right\}$$ when
$$L\left\{ {\cos \,\,\omega t} \right\} = {s \over {{s^2} + {\omega ^2}}}$$
GATE IN Subjects
EXAM MAP
Medical
NEET