Time domain initial & final value

[nanoha]

This is the formula for initial condition for f(t) by using F(s):
f(0)=lim x->infinity (sF(s))

and for f(infinity)=lim x->0 (sF(s))

So can anyone explain(by using the appropriate graph or derivative or anything) to me why the formula is inverse to each other. Why we need to use x -> infinity if we want to find f(0) but not f(infinity)....

 

[c36041254]

Hi there,
what you are asking for is a simple proof of initial and finial value theorem
go to this
https://en.wikipedia.org/wiki/Laplace_transform

and first understand how Laplace of first derivative is obtained and then Google for initial and final value theorem

 

[nanoha]

Thanks for the info... at least I know where should I start...
(I can't just google when I don't know the exact keyword)

 

[c36041254]

Hi there,
here is an another link **broken link removed**

 

[MrAl]

Hi there,

Another very simple explanation is as follows...

Since time is the inverse of frequency, and vice versa, it makes sense
that if you have a formula that depends on frequency the two domains
run opposite to each other.

In other words, for a period T and frequency F,

F=1/T
and
T=1/F

Note that T=0 when F->inf, and T->inf when F->0.

 

[nanoha]

Oh my God, I never realize about this before although I used the eq a lot...
Thanks a lot Mr. Al...

 

[MrAl]

Oh my God, I never realize about this before although I used the eq a lot...
Thanks a lot Mr. Al...

Hi there nanoha,

You are certainly welcome, and i apologize that i didnt even explain it
very clearly. I meant to say that if you have an equation that depends
on frequency and since T=1/F if you want the initial time solution you have
to make frequency F go to infinity (so that T goes to zero), and if you want
the final time solution again because T=1/F you have to let F approach zero
so that T goes toward infinity.

Take care and good luck with your studies...

 

[nanoha]

You are certainly welcome, and i apologize that i didnt even explain it
very clearly.

I think you should not apologize in the first place but it's me that need to thank you. Your first post is already enough for me. And thanks for the better explanation at the second post...