Page 235 - Engineering Mathematics Workbook_Final

Laplace Transforms

PROPERTIES OF LAPLACE 34. If F(s) is the Laplace transform of the
TRANSFORM function f(t) then Laplace transform

)
2
30 L (sin t = of 0  t f ( )d  is
1
( )
1 2 (a) F s
(a) (b) s
( s s + ) 1 ( s s + ) 4
2
2
1
( )
−
2 4 s 2 (b) F s − f ( ) 0
(c) (d) s
2
2
s 2 ( s + ) 4 2s ( s + ) 4
( )
(c) sF s − f ( ) 0
 sin2t 
31. L       =
 t  (d)  F ( ) s ds [GATE-2007 (ME)]
−
−
1
1
(a) cos s (b) cot s 35. The unilateral Laplace transform of
(c) cot − 1 s (d) tan − 1 s f(t) is 1 . The unilateral
2 2 s + 2 s + 1
 1 e t  Laplace transform of t f(t) is
−
32. L       = s
 t  (a) −
( s + 2 s + ) 1 2
 s − 1   s  
+
(a) log       (b) log       2s + 1
 s   s  (b) − 2
 s   s − 1  ( s + 2 s + ) 1
(c) log       (d) log      
 s − 1   s + 1  s
(c) 2
33. The Laplace transform of e t  cos t  ( s + 2 s + ) 1
is equal to … 2s + 1
(d)
−
s  ( s + 2 s + ) 1 2
(a)
(s  − ) + 2  2
[GATE-2012 (EC, EE, IN)]
+
s 
(b) 36. The Laplace transform of
(s  − ) + 2  2
f ( ) 2t = / t  is s − 3/ 2 . The Laplace
1
g
(c) transform of ( ) t = 1/ t  is
−
(s  ) 2
(a) 3s − 5/ 2 /2 (b) s − 1/ 2
(d) None (c) s 1/ 2 (d) s 3/ 2

[GATE-1997-EC] [GATE-2014-EE-SET 2]

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