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Outkast3r09 Group Title

Uncertainty ( Propogation of Errors)

  • one year ago
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  1. Outkast3r09 Group Title
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    say i have a function given by \[f(x)=\frac{v_1+v_2(v_3^3)}{YG}\]

    • one year ago
  2. Outkast3r09 Group Title
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    @JenniferSmart1 @jim_thompson5910

    • one year ago
  3. JenniferSmart1 Group Title
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    for what class is this?

    • one year ago
  4. Outkast3r09 Group Title
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    physics 2.. if i have 3 different avg velocities v1,v2 and v3 and \[U_t,U_d,U_Y,U_G\]

    • one year ago
  5. Outkast3r09 Group Title
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    should i find the uncertainty of each velocity? that would seem to give a rounding error though =/

    • one year ago
  6. Outkast3r09 Group Title
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    or would i go about with substituting in \[v=\frac{d}{t}\]

    • one year ago
  7. Outkast3r09 Group Title
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    @Jemurray3

    • one year ago
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    @TuringTest

    • one year ago
  9. JenniferSmart1 Group Title
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    @JamesJ

    • one year ago
  10. Outkast3r09 Group Title
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    if i switch to d/t|dw:1360620787006:dw|

    • one year ago
  11. Outkast3r09 Group Title
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    |dw:1360620861233:dw|

    • one year ago
  12. Outkast3r09 Group Title
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    then would i do for d1,t1,d2,t2,d3,t3,Y,and G?

    • one year ago
  13. Outkast3r09 Group Title
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    using partials of course

    • one year ago
  14. Outkast3r09 Group Title
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    |dw:1360620933162:dw|

    • one year ago
  15. Outkast3r09 Group Title
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    then using \[TUnc_{f(x)}=\sqrt{(\frac{\delta f}{\delta d_1}U_d})^2+(\frac{\delta f}{\delta t_1}U_t)^2+(\frac{\delta f}{\delta d_2}U_d)^2....\]... i feel you'd get strange units doing this =/

    • one year ago
  16. Outkast3r09 Group Title
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    but mayben ot since the other v terms cancel out in each partial

    • one year ago
  17. Outkast3r09 Group Title
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    any luck turing?

    • one year ago
  18. Outkast3r09 Group Title
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    my other idea was to find the uncertainties of each velocity, and then use those uncertainties in my final uncertainty but that would seem to set me up for round errors = not so accurate

    • one year ago
  19. TuringTest Group Title
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    Can't say I can really help here, sorry :(

    • one year ago
  20. Outkast3r09 Group Title
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    derp lol

    • one year ago
  21. Outkast3r09 Group Title
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    @jim_thompson5910

    • one year ago
  22. Jemurray3 Group Title
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    Yes, you're right. Generally speaking, if you have a function of a bunch of variables \[ f = f(x_i) \] Then the uncertainty in f is \[\sigma_f^2 = \sum_i \left(\frac{\partial f}{\partial x_i}\right) ^2\sigma_{x_i}^2\] This is true only if the variables xi are uncorrelated. If there is correlation between them, you must go to higher order error terms, but in this case that does not appear to be necessary.

    • one year ago
  23. Outkast3r09 Group Title
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    @jemurray3 so in other words i should do d1 d2 d3 partials and t1 t2 t3 partials

    • one year ago
  24. Jemurray3 Group Title
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    I don't see those variables in the expression you wrote. Whatever variables your function depends on, take the partials, multiply by the uncertainties, square them, and add them all up.

    • one year ago
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