I've been working on Laplace transform for a while. I can carry it out on calculation and it's amazingly helpful. But I don't understand what exactly is it and how it works. I google and found out that it gives "less familiar" frequency view.
My question is how does Laplace Transform give frequency view?
I don't understand the connection between $f(t)$ and $\mathscr{L} (f(t))$. For example:- let $f(t) = t$, $\mathscr{L}(t)={1 \over s^2}$
$f(t) $ gives time view but how does $1 \over s^2$ give the frequency view? Somebody help me to understand what exactly is it. Thank you!!
Can anyone explain it in some physical phenomenon? Like harmonic oscillator? $$ \ddot {x} + \omega_n x = f(t)$$