1
GATE ECE 1993
Fill in the Blanks
+2
-0
The Laplace transform of the periodioc function f(t) describe4d by the curve below, i.e., $$f\left( t \right) = \left\{ {\matrix{ {\sin \,t\,\,\,if\,\left( {2n - 1} \right)\pi \le t \le 2n\pi } \cr {0\,\,\,\,\,\,\,\,otherwise} \cr } } \right.$$
is _________. (fill in the blank), n is an integer.
2
GATE ECE 1988
MCQ (Single Correct Answer)
+2
-0.6
The Laplace transform of a function f(t)u(t), where f(t) is periodic with period T, is A(s) times the Laplace transform of its first period. Then
A
A(s) = s
B
A(s) = 1/(1-exp(-Ts))
C
A(s) = 1/(1+exp(-Ts))
D
A(s) = exp (Ts)
3
GATE ECE 1987
MCQ (Single Correct Answer)
+2
-0.6
Laplace transform of the functions t u(t) and u(t) sin(t) are respectively:
A
$${1 \over {{s^2}}},\,{s \over {{s^2} + 1}}$$
B
$${1 \over s},\,{1 \over {{s^2} + 1}}$$
C
$${1 \over {{s^2}}},\,{1 \over {{s^2} + 1}}$$
D
$$s,{s \over {{s^2} + 1}}$$
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