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anonymous
 3 years ago
Uncertainty ( Propogation of Errors)
anonymous
 3 years ago
Uncertainty ( Propogation of Errors)

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0say i have a function given by \[f(x)=\frac{v_1+v_2(v_3^3)}{YG}\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0@JenniferSmart1 @jim_thompson5910

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0for what class is this?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0physics 2.. if i have 3 different avg velocities v1,v2 and v3 and \[U_t,U_d,U_Y,U_G\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0should i find the uncertainty of each velocity? that would seem to give a rounding error though =/

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0or would i go about with substituting in \[v=\frac{d}{t}\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0if i switch to d/tdw:1360620787006:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1360620861233:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0then would i do for d1,t1,d2,t2,d3,t3,Y,and G?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0using partials of course

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1360620933162:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0then 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 =/

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0but mayben ot since the other v terms cancel out in each partial

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0my 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

TuringTest
 3 years ago
Best ResponseYou've already chosen the best response.0Can't say I can really help here, sorry :(

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Yes, 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.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0@jemurray3 so in other words i should do d1 d2 d3 partials and t1 t2 t3 partials

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I 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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