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
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    0
    hi,
    how to do laplace transform on that?
    is my work right?

    regards,
    stupid
     
  2. Georacer

    Moderator

    Nov 25, 2009
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    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
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    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
    782
    Your original answer is correct.

    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)}
     
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