Page 17 - LAPLACE TRANSFORM

1.3 Laplace Transform of a function by using Table (Linearity)

Example 3

Compute the following functions by using table of Laplace transform.

-2t
1. f(t) = t e
4
2. f(t) = t

3t
3 5t
3. f(t) = 5e + t e
4. f(t) = 7t + 8 sin 6t

2t
3 -4t
5. f(t) = 3 t e + 4 e cos 7t
-2t
2 3t
6. f(t) = 5 t e + 6 e sin 7t + cos 8t

SOLUTION

-2t
1. f(t) = t e
-2t
ʆ {f(t)} = ʆ {t e }
1 1
= .
1 +
=
( + ) 2
1 1
= .
= 1 2 +2
( +2) 2

1
-at
7 Exponent t e
( + ) 2

11