Simple check (book wrong)

Discussion in 'Homework Help' started by ihaveaquestion, Nov 4, 2009.

  1. ihaveaquestion

    Thread Starter Active Member

    May 1, 2009
    314
    0
    I'm pretty sure the book is wrong on this:

    Asked to find the initial and final values of

    G(s) = 3s^3+2s+10 / s(s+2)^2(s+3)

    initial-value theorem says that f(0)= lim(s->infinity) of sF(s) which comes out to 3 and I agree with that

    however for the final-value theorem I disagree....

    the book says its 0.833 but I believe it's 0.

    final-value theorem says f(infinity)=lim(s->0) of sF(s)

    If you divide 10/(2^2+3) thats 0.833, but that means you didnt multiply the numerator by s in the case... in other words:

    sG(s) = 3s^4+2s^2+10s / s(s+2)^2(s+3)

    You can see that as you take the limit of s approaching 0, the numerator will become 0 and the whole thing is 0...

    agree?
     
  2. StayatHomeElectronics

    Well-Known Member

    Sep 25, 2008
    864
    40
    f(infinity)=lim(s->0) of sF(s)

    G(s) = 3s^3+2s+10 / s(s+2)^2(s+3)

    sG(s) = s (3s^3+2s+10) / s (s+2)^2(s+3)
    sG(s) = (3s^3+2s+10) / (s+2)^2(s+3)

    you can simplify since both numerator and denominator have an s.

    If you do not simplify you would get 0 in both the numerator and denominator.
     
Loading...