Hello, i have a problem that i do not know where to begin with. It says to prove, using the Laplace Transform, that
Is it done using Euler's formula?
The main idea with using Laplace transforms is to transform the given equation into an algebraic one and simplify the algebraic equation (maybe by breaking it down into several fractions) and then transform it back using an inverse Laplace transform.
Do you have tables of Laplace and inverse Laplace transforms to help you carry out those operations?
A praticable way to realize the idea may be the following. Let's start writing...
(1)
.... where Si(*) is the 'Sine Integral Function'. Now is...
(2)
... so that...
(3)
... and is...
(4)
Now we can combine (1), (2), (3) and (4) and obtain...
(5)
In my opinion however the use of the Fourier Tranform and the 'Parseval's Identity' allows to obtain the result in a more confortable and also elegant way...
Kind regards