1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What am I doing wrong?

  1. Jun 23, 2010 #1
    What am I doing wrong???

    When you have an equation such as the one displayed in Equation 1 (see attached figure) and want to compute it by hand, you may rewrite it as Equation 2.

    Setting X and Y to the following values:

    X = Exp[-(n-1)/beta]
    Y = Exp[-T/alpha]

    I got Equation 3. Thereafter, I tried to transform it in the same way, and then I got Equation 4. However, Equation 3 and 4 are not the same. For alpha=360, beta=5, A1=10 and T=1, these two equations give very different curves, as you can see at the bottom of the image (Equation 3 represented as the purple curve, and Equation 4 represented as the blue line). What am I doing wrong?

    Thanks in advance,

    Estev√£o

    P.S.: Please, I really need help in this issue.
     

    Attached Files:

    Last edited: Jun 23, 2010
  2. jcsd
  3. Jun 24, 2010 #2

    uart

    User Avatar
    Science Advisor

    Re: What am I doing wrong???

    Here's a hint Lucas. Go back and have a look at how you derived equation 2 from equation 1. Notice that to get it in the form of a geometric series you had to factorize out the X's and Y's across the sum of multiple terms. Think about what that means about X and Y, they must be constants, neither can depend on "n".
     
  4. Jun 24, 2010 #3
    Re: What am I doing wrong???

    You are right! Thank you very much for the answer. However, now I have a new problem: how to simplify Equation 3 so I can compute it by hand?
     
  5. Jun 25, 2010 #4

    uart

    User Avatar
    Science Advisor

    Re: What am I doing wrong???

    Have you ever used Z-Transforms LucasGB? There are many ways to solve difference equations but z-transforms are one of the easiest.

    See : http://en.wikipedia.org/wiki/Z-transform

    I'll leave some of the work to you, but I get an answer that exactly matches your "red curve" and it's in the form of :

    [tex]A_n = \frac{A_1}{b-a} ( b^n - a^n ) [/tex]

    where "a" and "b" are constants in terms of your alpha, beta, T etc.
     
  6. Jun 25, 2010 #5
    Re: What am I doing wrong???

    It seems great, but I'm having a hard time searching for introdutory texts to Z-Transforms. Could you suggest one to me?
     
  7. Jun 25, 2010 #6
    Re: What am I doing wrong???

    LucasGB, I think there is no need of Z-transform.
    Look at the attached picture.
    I hope it will help you.
    (Sorry, in the picture, when it says "knowing that X(1)=0", it should say "knowing that X(1)=1"
     

    Attached Files:

    Last edited: Jun 26, 2010
  8. Jun 28, 2010 #7
    Re: What am I doing wrong???

    Thank you very much, Karlx. This is a very creative way to solve the equation. You and uart helped me a lot!
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook