Page 20 - LAPLACE TRANSFORM

A B 1
1 = . 2 2
= . − +

+
1 .
= 3! . 1 = −2 + 7 2
2
3+1 +4

= 3 [ 3! ] + 4 [ −2 ]
2
( +4) 3+1 ( −2) + 7 2
= 3 [ 1 2 3 ] + 4 [ −2 ]
2
( +4) 4 ( −2) + 49
18 4 −8
= +
2
( +4) 4 ( −2) + 49

e (n = 1,2,3 … . )
1 t n-1 -at 1
8 Exponent
(n−1)!
( + )

n -at
9 Exponent t e (n = 1,2,3 … . ) !
( + ) +1

(s + a)
-at
13 Decaying cosine e cos ωt
(s + a) + ꞷ 2
2

2 3t
-2t
6. f(t) = 5 t e + 6 e sin 7t + cos 8t

A B
2 3t
-2t
ʆ {f(t)} = ʆ {5 t e + 6 e sin 7t + 2 cos 8t}

= 5 [ ! ] + 6 [ ] + 2 [ ]
2
2
( − ) +1 ( + ) + 2 + 2

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