Here's the question you clicked on:
Outkast3r09
Uncertainty ( Propogation of Errors)
say i have a function given by \[f(x)=\frac{v_1+v_2(v_3^3)}{YG}\]
@JenniferSmart1 @jim_thompson5910
for what class is this?
physics 2.. if i have 3 different avg velocities v1,v2 and v3 and \[U_t,U_d,U_Y,U_G\]
should i find the uncertainty of each velocity? that would seem to give a rounding error though =/
or would i go about with substituting in \[v=\frac{d}{t}\]
if i switch to d/t|dw:1360620787006:dw|
|dw:1360620861233:dw|
then would i do for d1,t1,d2,t2,d3,t3,Y,and G?
using partials of course
|dw:1360620933162:dw|
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 =/
but mayben ot since the other v terms cancel out in each partial
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
Can't say I can really help here, sorry :(
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.
@jemurray3 so in other words i should do d1 d2 d3 partials and t1 t2 t3 partials
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.