Understanding Laplace Transformations: A Practical Guide and Real-Life Examples

[tabularasa]

I've posted this question already to Math forum but no success to get answer that I understand. This is trivial question about fundamental Laplace transformation. My goal is to understand what is Laplace transformation and when and why to use Laplace transformation.

I'm looking practical example of Laplace. I think that I don't quite understand Laplace without some real life concrete example. Is this right thread/forum to looking for that? Algebra is not a problem. But still this S-constant is and also what Laplace transformed function actually represents.

If I have that very basic linear function 2x and I Laplace transform that:
$$\mathcal{L} [2x](s) = 2 \mathcal{L}[x](s)= 2 \cdot \frac 1{s^2} = \frac 2{s^2}$$

Ok, now if x goes to -10 to 10 and I want to know what that Laplace function gives answer for instance when x=5. What will be the result and what that result represents?

 

[HallsofIvy]

I have no idea what you mean by "x goes to -10 to 10" or "when x= 5". The Laplace transform is a transform of the function f(x)= 2x. It makes no sense ask "what is the Laplace transform when x= 5". The Laplace transform of a function of x is a function of s. It can be evaluated at values of s, not x.

 

[tabularasa]

Removed To New Thread. Question Changed