Page 65 - LAPLACE TRANSFORM

Example 1

Find the Inverse Laplace Transform by using Partial Fraction.

s
4 + 2
F (s ) =
s
s
( + 2 )( − ) 1

4 s + 2 = A + B
s ( + 2 )( s − ) 1 s ( + 2 ) s ( − ) 1
4 s + 2 = A( s − ) 1 + B( s + 2 )......... ... equation 1
if s ( + 2 ) = 0
s = − 2
Substitude s = − 2 int o equation1

4 (− 2 ) + 2 = A(− 2 − ) 1 + B 0( )
− 6 = A(− ) 3
− 6
A = = 2
− 3
If s ( − ) 1 = 0
s = 1
Substitude s = 1 int o equation1
4 ) 1 ( + 2 = A 0( ) + B 1( + 2 )
6 = B 3( )
6
B = = 2
3
2 2
∴ Partial Fraction = +

s ( + 2 ) s ( − ) 1
 2   2 
1
−
1
−
∴ Inverse Laplace Transform = L   + L  
 s ( + 2 )   s ( − ) 1 
= 2 e − 2 t + 2 e t

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