Page 34 - LAPLACE TRANSFORM
P. 34
Example 2
By using the First Shifting Theorem determine the Laplace Transforms.
{ }
at
te
L
f ( t = t
)
1
t
{ (tf } ) = L {}=
s 2
∴ { e at f (t ) = at • } t
} { eL
1
=
( − ) 2 2
s
Example 3
By using the First Shifting Theorem determine the Laplace Transforms.
at
f ( t) = e sin bt
b
L ( )} = L {sin bt } =
{ f t
2
s + b 2
t
at
∴L { fe at ( )} = L { e sin bt }
b
= 2 2
(s − ) a + b
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