Page 21 - LAPLACE TRANSFORM

A B
1 = 1 .
= . + + 2
2
−
1 7
2! 1 = .
2
= . +2 + 7 2
2+1 −3

= 5 [ 2! ] + 6 [ 7 ] + 2 [ ]
2
2
( −3) 2+1 ( +2) + 7 2 + 8 2

= 5 [ 1 2 ] + 6 [ 7 ] + 2 [ ]
2
2
( −3) 2+1 ( +2) + 7 2 + 8 2

= 10 + 42 + 2
2
2
( −3) 3 ( +2) + 49 + 64

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

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

11 Cosine cos ωt
2
+ 2

ꞷ
-at
12 Decaying sine e sin ωt
2
(s + a) + ꞷ 2

15