Page 19 - LAPLACE TRANSFORM

-at
6 Exponent e 1
+

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

4. f(t) = 7t + 8 sin 6t

ʆ {f(t)} = ʆ {7t + 8 sin 6t}

1
= 7 [ ] + 8 [ ]
2
2 + 2
7
= + 8 [ 6 ]
2
2 + 6 2
7
= + 48
2
2 + 36
1
3 Linear t
s 2

10 Sine sin ω t
2
+ 2

A B
3 -4t
5. f(t) = 3 t e + 4 e cos 7t
2t
2t
3 -4t
ʆ {f(t)} = ʆ {3t e + 4 e cos 7t}

= 3 [ ! ] + 4 [ − ]
2
( + ) +1 ( − ) + 2

13