Page 52 - LAPLACE TRANSFORM

s + 8 = A ( + ) ( + ) + B ( + ) + C( + )
2
s + 8 = A ( + 9 + 20) + B ( + 4) + C ( + 10 + 25)
2
2
2
s + 8 = A + 9 + 20 + B + 4 + C + 10 + 25

2
s ; 0 = A + C ................................. (1)
1
s ; 1 = 9A + B + 10C ........................... (2)
0
s (without s); 8 = 20A + 4B + 25C ....................... (3)
B = −3 , C = 4

0 = A + C ................................. (1)

A = − C = − 4

f(t) = + +
( +5) 1 ( +5) 2 ( +4)

= − + − +
( +5) 1 ( +5) 2 ( +4)

= -4 ( ) − 3 ( ) + 4 ( )
( +5) 1 ( +5) 2 ( +4)
-5t
-4t
-5t
= − e – 3t e + 4 e

s − 12
F
5. (s ) =
s (s 2 + ) 9

2
s – 12 = A(s + 9) + (Bs + C) (s)

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