# need help on laplaceX of imaginary #

Discussion in 'Homework Help' started by stupid, Oct 25, 2010.

1. ### stupid Thread Starter Active Member

Oct 18, 2009
81
0
hi,
how to do laplace transform on that?
is my work right?

regards,
stupid

File size:
232.1 KB
Views:
30
2. ### Georacer Moderator

Nov 25, 2009
5,151
1,266
Is "i" an index of t or another constant?

If i is a constant, then you are correct.

3. ### stupid Thread Starter Active Member

Oct 18, 2009
81
0
hi Georacer,
i denotes imaginary sign like the operator j
so, 8ti is an imaginary no.

thanks

Last edited: Oct 25, 2010
4. ### Georacer Moderator

Nov 25, 2009
5,151
1,266
Oh! of course, how silly of me. I am surprised however, since I don't recall seeing t and i in the same time function expression befor.

5. ### stupid Thread Starter Active Member

Oct 18, 2009
81
0
u mean it is illegitimate?
i recall e^jβt=1

does that prove the subject in hand?

6. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
784

An interesting illustrative case in point is ....

$L[cos(\omega t)+jsin(\omega t)]=L[e^{j\omega t}]$

$L[e^{j \omega t}]=\frac{1}{(s-j\omega)}$

$\frac{1}{(s-j\omega)}=\frac{s+j\omega}{(s^2+\omega^2)}=\frac{s}{(s^2+\omega^2)}+\frac{j\omega}{(s^2+\omega^2)}$

Equating the real and imaginary parts gives

$L[cos(\omega t)]=\frac{s}{(s^2+\omega^2)}$

$L[sin(\omega t)]=\frac{\omega}{(s^2+\omega^2)}$