How to move forward with Laplace transform of e^(i(5t))

Jimena Hatfield

Jimena Hatfield

Answered question

2022-09-11

How to move forward with Laplace transform of e i ( 5 t )
L { e i ( 5 t ) } = 0 e s t e i ( 5 t )   d t = 0 e t ( s 5 i )   d t
Doing the change of variables u = t ( s 5 i ) = t ( 5 i s ), we get
0 e t ( s 5 i )   d t

Answer & Explanation

Yasmin Lam

Yasmin Lam

Beginner2022-09-12Added 13 answers

We have
0 e ( s 5 i ) t d t = [ e ( s 5 i ) t s 5 i ] 0 = 1 s 5 i [ e 5 i t e s t ] 0 = 1 s 5 i [ 0 1 ] = 1 s 5 i
since | e 5 i t / e s t | 1 / e s t 0 as t

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