laplce
- Thread starter jomex42
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could you plss show me the the right exact solution of how the upper function become the laplace of the lower function plssss help my proff want me to do it
Please write the mathematical description of Laplace transform (the integral form).
If your textbook or class-note does not describe it - do a google search.
HallsofIvy
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Okay, with \(\displaystyle f(t)= \frac{1}{t} sin(\alpha t)\), the Laplace transform is
\(\displaystyle \int_0^\infty \frac{1}{t} sin(\alpha t) e^{-st} dt\)
That looks pretty difficult to me! I might be inclined to try writing \(\displaystyle sin(\alpha t)\) as \(\displaystyle \frac{e^{i\alpha t}- e^{-i\alpha t}}{2i}\) and combine that with the \(\displaystyle e^{-st}\).
\(\displaystyle \int_0^\infty \frac{1}{t} sin(\alpha t) e^{-st} dt\)
That looks pretty difficult to me! I might be inclined to try writing \(\displaystyle sin(\alpha t)\) as \(\displaystyle \frac{e^{i\alpha t}- e^{-i\alpha t}}{2i}\) and combine that with the \(\displaystyle e^{-st}\).
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