Page 24 - LAPLACE TRANSFORM

Example 3

t)
t 4
Find Laplace Transform, F(s) of given functions f ( = 2 e sin t 4
ft 2e 4t sin 4t
( ) =

Refer to the table of Laplace Transform :-
f (t ) = 2L {e 4t sin 4t }
4
= [ 2 ]
2
( −s ) 4 + 4 2
8
=
( −s 4 )( −s ) 4 + 16
8
=
s 2 − 4 − ss 4 + 16 + 16
8
=
8 +
s 2 − s 32

Example 4

3 −
2t
Find Laplace Transform, F(s) of given functions ( )f t = te 2t + 4e − 4t cos3t + 3e
3 −
f ( ) = t te 2t + 4e − 4t cos3t + 3e 2t
Refer to the table of Laplace Transform :-

= L { et 3 − 2t }+ 4L {e − 4t cos 3t }+ 3L {e 2t }
! 3 ( + ) 4 1
s
= [ ] + [ 4 ] + [ 3 ]
( + ) 2 3+ 1 ( + ) 4 2 + 3 2 ( − ) 2
s
s
s
6 4 + 16 3
s
= [ ] + [ ] + [ ]
s
( + ) 4 4 ( + 4 s ) 4 + 9 s − 2
)( +
s
s
6 4 + 16 3
= [ ] + [ ] + [ ]
s
( + ) 4 4 (s 2 + 4 + ss 4 + 16 + ) 9 s − 2
s
6 4 + 16 3
= [ ] + [ ] + [ ]
( + ) 4 4 s 2 + s 25 s − 2
s
8 +
17