Page 237 - Engineering Mathematics Workbook_Final

Laplace Transforms

45. The inverse Laplace transform of the 2 4
s + 5 (a) s + 1 (b) s + 1
function is ….
(s + 1 )(s + ) 3
4 2
(c) (d)
4
2
t −
t −
(a) 2e − e − 3t (b) 2e + e − 3t s + 1 s + 1
t −
t −
(c) e − 2e − 3t (d) e + 2e − 3t [GATE-2013-ME]
LAPLACE TRANSFORM OF
[GATE-1996-EC]
PERIODIC FUNCTIONS
46. The Laplace transform of a function

1 49. The Laplace Transform of the
f(t) is . The function f(t) is periodic function f(t) described by the
s 2 (s + ) 1 curve below

+
+
t −
t −
(a) t − 1 e (b) t + 1 e  sin , t if (2n − ) 1  t 2n   (n = 1,2,3,... )

t −

−
+
t
(c) 1 e (d) 2t + e f ( ) t =  0 otherwise

APPLICATION OF LAPLACE
TRANSFORM IN DIFFERENTIAL
EQUATION

47. Solve the initial value problem [GATE-1993 (ME)]
2
d y − 4 dy + 3y = 0 with y = 3 and
dx 2 dx INITIAL & FINAL VALUE THEOREM
dy = 7 at x = 0 using the Laplace 5s + 2 23s + 6

dx 50. If L ( ) f = F ( ) s = 2
transform technique. ( s s + 2s + ) 2
( )
then lim f t = _____ .
[GATE-1997-ME] t→ 

48. The function f(t) satisfies the 2
If F ( ) s = then
2
d f s (1 s+ )
differential equation + f = 0
dt 2 lim f ( ) t = _____ where L(f(t)) =
and the auxiliary conditions, f(0) = 0, t→ 
df ( ) 0 = . The Laplace transform of F(s).
4
dt If  f c ( 2 s + ) 1
L
f(t) is given by ( ) = s + 2 2s + 1 then f(0*)
f
and ( )  given by ….

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