Page 58 - LAPLACE TRANSFORM

2t
= − e + e 10t

6 + 2
s
F
2. (s ) =
( + ) 5 3
s

6 + 2
s
F (s ) = = + +
( + ) 5 3 ( +5) 1 ( +5) 2 ( +5) 3
s

6s + 2 = A ( + ) + B ( + ) + C

when (s + 5) = 0
s= − 5; 6(−5) + 2 = A ( + 5) + B( + 5) + C
2
−30 + 2 = C

C = -28

2
6s + 2 = A ( + 5) + B ( + 5) + C
2
6s + 2 = A ( + 10 + 25) + B ( + 5) + C
2
6s + 2 = A + 10 + 25 + Bs + 5B + C

2
s ; 0 = A ..................................... (1)
1
s ; 6 = 10A + B ............................ (2)
0
s (without s); 2 = 25A + 5B + C ..................... (3)

C = −28 , A = 0

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