Page 47 - LAPLACE TRANSFORM

SOLUTION

s + 10 s + 10
F
1. (s ) = =
4 −
s
(s 2 − s 12 ) ( + 2 )( − ) 6
s
s + 10
=
)( −
( + 2 s ) 6
s

= + @ +
( +2) ( −6) ( − ) ( + )

multiply each side with denominator;

s + 10 = A (s − 6) + B (s + 2)

when (s + 2) = 0

s= −2; s + 10 = A (s − 6) + B (s + 2)

−2 + 10 = A (−2 − 6) + B (−2 + 2)

8 = A (−8) + 0

= = −1
−

when (s − 6) = 0

s= 6;

s + 10 = A (s − 6) + B (s + 2)

6 + 10 = A (6 − 6) + B (6 + 2)

16 = 0 + B (8)

= =

36