Page 68 - LAPLACE TRANSFORM

s
s
s
2 + 3 = A (s 2 − 4 + ) 4 + B (s 2 − s − ) 2 + c ( + ) 1
RHS

RHS LHS
Equation 1

s 2 A+B
Equation 1 0

s -4A-B+C
2

constant 4A-2B+C
3

From equation 1……………………

A + B = 0
1 + B =

9 0
1
B = −
9

1 1 7
Therefore the Partial Fraction : − +
( 9 s )1+ ( 9 − ) 2 ( 3 − ) 2 2
s
s

Inverse Laplace Transform :

1 1 7
= L − 1 − L − 1 + L − 1
s
s
( 9 + ) 1 ( 9 − ) 2 ( 3 − ) 2 2
s
1 1 7
t 2
t −
= e − e + te t 2
9 9 3 #

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