Page 22 - LAPLACE TRANSFORM

1.4 Laplace Transform using First Shift Theorem

If ʆ {f(t)} = F(S);

-at
ʆ {e f(t)} = F(s+a) ; change s to s= (s+a)

at
ʆ {e f(t)} = F(s−a) ; change s to s= (s−a)

Example 4

Compute the following functions using First Shift Theorem.

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

SOLUTION

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

ʆ {t} = (refer to table)
s 2

3 Linear t

-2t
ʆ {t.e } = change s to s= (s+2)
(s) 2

=
( + )

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