Page 34 - LAPLACE TRANSFORM

SOLUTION

1) F(S) = +

− +

-1
-1
f(t) = ʆ {F(S)} = ʆ { +3 }
2
−4 + 13

A=1, B=4, C=13
+3
=

2
( − 2) + 3 2 2 2
(s ± ) + (C − ( ) )

2
2
2
( − 2)+5 (s − ) + (13 − ( ) ) = (s − ) + (9)
=
2

( − 2) + 3 2
2
= (s − ) + (3)
2

( − 2) 5
= +

2

2
( − 2) + 3 2 ( − 2) + 3 2

5
2t
= e 3 + [ 3 ]

2
3 ( − 2) + 3 2

5
2t
2t
= e 3 + e 3
3

2) F(S) = +

− +

-1
-1
f(t) = ʆ {F(S)} = ʆ { +8 }
2
−6 + 34

A=1, B=6, C=34
+ 8
=

2
( −3) + 5 2 (s ± ) + (C − ( ) )
2
2

2 2 2
( − 3) +11 (s − ) + (34 − ( ) ) = (s − ) + (25)
=
2

( −3) + 5 2
2
2
= (s − ) + (5)

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