Page 69 - LAPLACE TRANSFORM

Example 4

Find the Inverse Laplace Transform by using Partial Fraction.
s
F (s ) =
s
( + 1 )(s 2 + ) 1
s A Bs + C
L 1 − { } = +
s
( + 1 )(s 2 + ) 1 ( + ) 1 (s 2 + ) 1
s
= As (s 2 + ) 1 + (Bs + C )( +s 1 …………………….equation (1)
)
if s = − 1

1=− A ((− ) 1 + ) 1
2
− 1= ) 2 ( A

A = − 1

2
Expand equation (1)

RHS

2
s = A( s + )1 + Bs + Bs + C
2

RHS LHS

s 2 A+B 0 Equation 1

s B + C 1 Equation 2

constant A + C 0

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