Page 35 - LAPLACE TRANSFORM
P. 35
Example 4
By using the First Shifting Theorem determine the Laplace Transforms.
f ( t) = e − t 3 sin t 2
2
{ f t
L ( )} = L {sin 2t }=
s 2 + 2 2
2
∴L { e − t 3 sin } t 2 =
2
s
( + ) 3 + 4
2
=
s 2 + 6 +s 13
Example 5
By using the First Shifting Theorem determine the Laplace Transforms.
(tf ) = L {e 4t cosh 4t )
s
f ( t) = L{cosh 4 t} =
2
s − 4 2
s ( − ) 4
4
e cosh
t 4
L{
=
t}=
s ( − ) 4 2 − 16
s ( − ) 4 s ( − ) 4
= =
2
s ( − 4 )( s − ) 4 − 16 s − s 4 − 4 s 16 −+ 16
s ( − ) 4
=
2
s − s 8
28
