Page 70 - LAPLACE TRANSFORM

From equation 1……………..
A + B = 0

1
(− ) + B = 0
2

B = 1
2

From equation 2………………..

B + C = 1
1
( ) + C = 1
2
C = 1− 1
2

C = 1
2

1 1 1
Therefore value of =A − , B = , C =
2 2 2

Therefore the Partial Fraction :-

s
s 1 1 ( + ) 1
= − + ( )

s
( + 1 )(s 2 + ) 1 ( 2 s + ) 1 2 (s 2 + ) 1
Inverse Laplace Transform:-
1 1 ( +s ) 1
L 1 − − + L 1 − ( 2 )
( 2 +s ) 1 2 (s + ) 1
1 1 s 1
= − e −t + L 1 − { }+ L 1 − { }
2 2 s 2 + 1 s 2 + 1

1 1 1
t −
= − e + cos t + sin t
2 2 2 ##

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