Page 45 - LAPLACE TRANSFORM

Example 5

Find the Laplace Transform using Multiplication by of

the followings:-

( 2 ) Formula Quotient Rule

s du dv
Lf (t ) = L {cos 2t }= v − u
s 2 + 4 d = ds ds
d  s  2
t
L { cos 2t }= ( − )1   ds v
ds s 2 + 4 

*use Queotient Rule to solve this question.
u = s v = s + 4
2
du = 1 dv
ds ds = s 2
By using the Third Multiplication of t Theoram, find the
n
d = (s 2 + 4 )( ) 1 − (s )( 2s )
ds (s 2 + ) 4 2

2
2s
s
v = du + 4 − dv 2
u
) 4
2
d = ds (s − 2 + ds
ds = − s v 2 2 + 4
(s 2 + ) 4 2
Therefore, Laplace Transform of the

 − s 2 + 4 
t
L { cos 2t } (−= ) 1   following.:-
 (s 2 + ) 4 2 
s 2 − 4 2
t)
=
f ( = t 2 e t 5 [Ans: 3 ]
s
2
2
(s + ) 4 ( − ) 5

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