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Outkast3r09

  • one year ago

Uncertainty ( Propogation of Errors)

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

  2. Outkast3r09
    • one year ago
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    @JenniferSmart1 @jim_thompson5910

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

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

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

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

  7. Outkast3r09
    • one year ago
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    @Jemurray3

  8. Outkast3r09
    • one year ago
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    @TuringTest

  9. JenniferSmart1
    • one year ago
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    @JamesJ

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

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

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

  13. Outkast3r09
    • one year ago
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    using partials of course

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

  15. Outkast3r09
    • one year ago
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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 =/

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

  17. Outkast3r09
    • one year ago
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    any luck turing?

  18. Outkast3r09
    • one year ago
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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

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

  20. Outkast3r09
    • one year ago
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    derp lol

  21. Outkast3r09
    • one year ago
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    @jim_thompson5910

  22. Jemurray3
    • one year ago
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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.

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

  24. Jemurray3
    • one year ago
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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.

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