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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? $$ \ddot {x} + \omega_n x = f(t)$$

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    Have a look at this: http://math.stackexchange.com/questions/6661/laplace-transformations-for-dummies2012-08-10
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    looks like i should study Fourier Transform to understand it.2012-08-10
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    http://www.cambridge.org/us/features/chau/webnotes/chap2laplace.pdf2012-08-10
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    here is additional link http://www.phy.duke.edu/~hx3/physics/FourierLaplace.pdf2012-08-10
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    It's the same thing as with generating functions in combinatorics: It's a **very helpful** formal device, but for heaven's sake don't think that it has **any** intuitive physical, analytical, or geometrical meaning.2014-07-15

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