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Question about uncertainties

  1. Sep 26, 2008 #1
    (First post. Go easy on me, mods :D)
    EDIT: Seems I got the wrong forum. If a mod could be so kind to move it, I'd appreciate it :P

    Hi everyone!

    I'm working on a formal lab report for my physics class, and after propagating my uncertainties into a formula, I got an even smaller uncertainty relative to the original uncertainties (one of the indep. variables was 9% while my propagated uncertainty was 6%)

    Is this possible in ANY case?

    If it's not, I will post more information about the equations I'm using. I already spent 2 hours looking at all the numbers and using mathematica to calculate the results for me, and I just don't know what could be wrong with it (if there's even anything wrong with it).

    Thanks for your help,

    KodeK
     
    Last edited: Sep 26, 2008
  2. jcsd
  3. Sep 26, 2008 #2

    mathman

    User Avatar
    Science Advisor
    Gold Member

    Yes. In general if the random variables are independent, the uncertainties tend to smooth out.
     
  4. Sep 26, 2008 #3
    Hmm, I'd like to show you the equations I'm using just to get an okay so I know I'm doing this right. How would I copy mathematica's LaTeX output and paste it on the site? I don't want to have to copy an in-line equation :P
     
  5. Sep 26, 2008 #4
    Here's a screenshot of the problem I'm having:

    [​IMG]
     
  6. Sep 26, 2008 #5
    Yes, the errors can become less if the derivatives are small. If you evaluate a function f of independent variables x1, x2, ..., with respective errors dx1, dx2, ..., then the error in f is:

    df = sqrt[df1^2 + df2^2 + ...]

    where

    df1 = f(x1 + dx1/2, x2,...) - f(x1 - dx1/2, x2,...)


    df2 = f(x1, x2+dx2/2,...) - f(x1, x2 - dx2/2,...)

    etc.
     
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