How do I find the laplace transformation of i(t)=(t)(e^t)(sinkt)?

[mak_wilson]

please help me with this question

Find the laplace transformation of this function

i(t)=(t)(e^t)(sinkt)

i really don't know how to do!

 

[meister]

The Laplace Transform is defined as:

Y(s) = \int_{0}^{\infty} e^{-st}y(t)dt

where y(t) is the function you wish to find the Laplacian of.

In this example, the integral would be:

\int_{0}^{\infty} te^{-st}e^tsin(kt)dt

...which is unbelievably ugly.

Have you learned about convolution yet? This is a pretty nasty problem, unless I'm missing something, which it seems probable that I am.

 

[mak_wilson]

thz

You didnt miss anything, i can do up to this stage, but it contain 3 t in it, I don't really know how to solve it!

 

[arildno]

1. Since the integral of the e^((1-s)t)*sin(kt) will "rotate" during integration by parts (i.e. you will gain back a multiple of what you began integrating), evaluating the integral of this function alone should pose no problems.
(Assuming s>1, that is)

2. You can now go back to the original problem, using integration by parts to eliminate the t-factor.

3. Alternatively, you might use the complex exponential as a simplifying measure.

 

[quantumdude]

3. Alternatively, you might use the complex exponential as a simplifying measure.

That's what I would do, too. The beautiful thing about that is that, not only is it a lot easier to calculate, but it also gives you TWO Laplace transforms simultaneously.

mak_wilson, I would recommend that you take this suggestion. Make the replacement:

sin(kt)--->e^ikt

and take the imaginary part at the end.

 

[Max0526]

solution

Here is a solution,
Max.

 

[mak_wilson]

thank You~~