Page 80 - LAPLACE TRANSFORM

Expand equation 1 to find value of B & C

2
2
3 = A( s + )9 + Bs + cs + Bs c +

RHS LHS

S 2 A+B 0

s C+B 0
constant 9A+C 3

From equation 1………………. From equation 3…………..
A
A + B = 0 9 +C = 3

3 + B = 0 (9 3 ) +C = 3
10 10
3 3
B = − C =
10 10

Therefore the partial fraction:-

3 3 − s 3
3 +

L 1 − = = +
( +
(s 2 + 9 s ) 1 10 s ) 1 10 (s 2 + ) 9
)( +
3 1 s 1
= [ − + ]
10 ( +s ) 1 ( +s 2 ) 9 ( +s 2 ) 9

Inverse Laplace Transform :-

3 1 s 1
= L -1 [ − + ]
10 ( +s ) 1 ( +s 2 ) 9 ( +s 2 ) 9

= 3 e − 3 cos t 3 + 1 sin t 3
t −
10 10 10 ##

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