Page 23 - LAPLACE TRANSFORM

Example 1

Find Laplace Transform, F(s) of given functions.

f (t ) = 5 + 3e − 2t − 5t 2

Refer to the table of Laplace Transform :-

f (t ) = } 5 { L + 3L {e − 2t }− 5L {t 2 }

5 1 ! 2
= + [ 3 ] − [ 5 ]
s ( +s ) 2 s 2+ 1

5 3 10
= + −
s (s + ) 2 s 3

Example 2

Find Laplace Transform, F(s) of given functions.

f ( t) = e 4 t 2 + 4 sin t 4

Refer to the table of Laplace Transform:-

= L { }+ Le 2t { sin4 4t }
4
= 4L { } 4Le 2t + {sin 4t }

 1   4 
= 4  + 4 
s
 − 2   s 2 + 16 
4 16
= +
s − 2 s 2 + 16

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