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

regards,
stupid

 

Is "i" an index of t or another constant?

If i is a constant, then you are correct.

 

hi Georacer,
i denotes imaginary sign like the operator j
so, 8ti is an imaginary no.

thanks

Is "i" an index of t or another constant?

If i is a constant, then you are correct.

 

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.

 

u mean it is illegitimate?
i recall e^jβt=1

does that prove the subject in hand?

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.

 

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

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

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