Page 71 - LAPLACE TRANSFORM

Example 5

Find the Inverse Laplace Transform by using Partial Fraction.

7
F (s ) =
s 2 − 16

7 A B
= +
s
s
s 2 − 16 ( + ) 4 ( − ) 4

7 = A ( − ) 4 + B ( + ) 4 ……………………………equation (1)
s
s
if s = − 4

7 = A (− 4 − ) 4 + B (− 4 + ) 4
7 = A (− ) 8
7
A = −
8

if s = 4

7 = A 4 ( − ) 4 + B 4 ( + ) 4
7 = ) 8 ( B

7
B =
8

Partial Fraction :-

7 = − 7 + 7

s
s
s 2 − 16 ( 8 + ) 4 ( 8 − ) 4
Inverse Laplace Transform :-

7 7 7
L − 1 2 = L − 1 { }+ L − 1 { }
s
4
s
s − 16 ( 8 + ) ( 8 − ) 4
7 7
t 4
= − e − t 4 + e
8 8

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