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Outkast3r09

  • 2 years ago

Uncertainty ( Propogation of Errors)

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  1. Outkast3r09
    • 2 years 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
    • 2 years ago
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    @JenniferSmart1 @jim_thompson5910

  3. JenniferSmart1
    • 2 years ago
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    for what class is this?

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

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

  7. Outkast3r09
    • 2 years ago
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    @Jemurray3

  8. Outkast3r09
    • 2 years ago
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    @TuringTest

  9. JenniferSmart1
    • 2 years ago
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    @JamesJ

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

  11. Outkast3r09
    • 2 years ago
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    |dw:1360620861233:dw|

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

  13. Outkast3r09
    • 2 years ago
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    using partials of course

  14. Outkast3r09
    • 2 years ago
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    |dw:1360620933162:dw|

  15. Outkast3r09
    • 2 years 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
    • 2 years ago
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    but mayben ot since the other v terms cancel out in each partial

  17. Outkast3r09
    • 2 years ago
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    any luck turing?

  18. Outkast3r09
    • 2 years 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
    • 2 years ago
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    Can't say I can really help here, sorry :(

  20. Outkast3r09
    • 2 years ago
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    derp lol

  21. Outkast3r09
    • 2 years ago
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    @jim_thompson5910

  22. Jemurray3
    • 2 years 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
    • 2 years ago
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    @jemurray3 so in other words i should do d1 d2 d3 partials and t1 t2 t3 partials

  24. Jemurray3
    • 2 years 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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