Page 234 - Engineering Mathematics Workbook_Final

Laplace Transforms

2
−
−
+
26. Laplace transform of (a bt ) where a b e s (a b )
(a) (b)
‘a’ and ‘b’ are constants is given by: S S
−
2
(a) (a bs+ ) (c) e − as − e − bs (d) e ( s a b )
S S
1
(b) [GATE-2015-EC-SET 2]
(a bs+ ) 2

29. If x(t) is as shown in the figure, its
a 2 2ab 2b 2 Laplace transform is
(c) + +
s s 2 s 3

a 2 2ab b 2
(d) + +
s s 2 s 3

27. The Laplace Transform of the

following function is
 sint for 0 t 



f ( ) t = 
 0 for t  (a) 2e + 5s + 2e − 5s


s 2
1
(a) for alls > 0 + 5s − 5s
+
+
1 s 2 (b) 2e − 4 2e
s 2
1
(b) for alls <  + −
+
+
1 s 2 2e 5s − 2 2e 5s
(c)
s 2
+
1 e − ks
(c) for alls > 0 + 5s − 5s
+
+
1 s 2 2e + 4 2e
(d)
s 2
e − ks
(d) for alls > 0
+
1 s 2 [EEE-2018 (EC)]
[GATE-2002]
28. The bilateral Laplace transform of a
 1if a t b



function ( ) t =  is
f
 0 otherwise


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