0
$\begingroup$

Could someone show me explicitly what is going in the first line? I am confused as I have learnt Laplace transformations but I cannot figure out which Laplace transformation this is.. and the (a) in the first line, is that variable of the Laplace?

enter image description here

$\endgroup$

1 Answer 1

1
$\begingroup$

The Laplace transform of a function $f(t)$ is defined as

$$\mathcal{L}\{f\}(a)=\int_0^\infty f(t)e^{-at}\,dt$$

where $a$ denotes the parameter of the integral (i.e. $a$ appears in the evaluation).

In your case, for the first line, they set $f(t)=\sin(bt)/t$.

For the second equality, the frequency domain integration property was used.

$\endgroup$
2
  • $\begingroup$ what is the frequency domain integrration ppty? $\endgroup$ Commented Sep 24, 2020 at 1:59
  • $\begingroup$ You can find a proof here and is listed as a property here. Usually, to compute laplace transforms, lookup tables are used. See this. $\endgroup$
    – kiyomi
    Commented Sep 24, 2020 at 2:01

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .