Time domain initial & final value

N

nanoha

New Member

• Sep 11, 2008

• #1

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)....

 

C

c36041254

Member

• Sep 12, 2008

• #2

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

 

N

nanoha

New Member

• Sep 12, 2008

• #3

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)

 

Last edited: Sep 12, 2008

C

c36041254

Member

• Sep 13, 2008

• #4

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

 

M

MrAl

Well-Known Member

Most Helpful Member

• Sep 16, 2008

• #5

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.

 

N

nanoha

New Member

• Sep 16, 2008

• #6

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

 

M

MrAl

Well-Known Member

Most Helpful Member

• Sep 17, 2008

• #7

nanoha said:

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

Click to expand...

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...

 

Last edited: Sep 17, 2008

N

nanoha

New Member

• Sep 18, 2008

• #8

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

Click to expand...

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...