Page 51 - LAPLACE TRANSFORM

f(t) = + + = + +
( +3) 1 ( +3) 2 ( +3) 3 ( +3) 1 ( +3) 2 ( +3) 3

= ( ) + 6 ( )
( +3) 2 ( +3) 3
-3t
e
= t e + 6 1 t 3-1 -3t
(3−1)!
-3t
= t e + t e
2 -3t

s + 8
F
4. (s ) =
( + ) 5 2 ( + ) 4
s
s

s + 8 = A ( + ) ( + ) + B ( + ) + C( + )

when s= − 5;

s + 8 = A ( + ) ( + ) + B ( + ) + C( + )
− 5 + 8 = B (− 5 + 4)

= − 3

when s= − 4;

2
1
s + 8 = A ( + 5) ( + 4) + B ( + 4) + C( + 5)
2
− 4 + 8 = C(−4 + 5)
=

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