## Outkast3r09 2 years ago Uncertainty ( Propogation of Errors)

1. Outkast3r09

say i have a function given by $f(x)=\frac{v_1+v_2(v_3^3)}{YG}$

2. Outkast3r09

@JenniferSmart1 @jim_thompson5910

3. JenniferSmart1

for what class is this?

4. Outkast3r09

physics 2.. if i have 3 different avg velocities v1,v2 and v3 and $U_t,U_d,U_Y,U_G$

5. Outkast3r09

should i find the uncertainty of each velocity? that would seem to give a rounding error though =/

6. Outkast3r09

or would i go about with substituting in $v=\frac{d}{t}$

7. Outkast3r09

@Jemurray3

8. Outkast3r09

@TuringTest

9. JenniferSmart1

@JamesJ

10. Outkast3r09

if i switch to d/t|dw:1360620787006:dw|

11. Outkast3r09

|dw:1360620861233:dw|

12. Outkast3r09

then would i do for d1,t1,d2,t2,d3,t3,Y,and G?

13. Outkast3r09

using partials of course

14. Outkast3r09

|dw:1360620933162:dw|

15. Outkast3r09

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

but mayben ot since the other v terms cancel out in each partial

17. Outkast3r09

any luck turing?

18. Outkast3r09

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

Can't say I can really help here, sorry :(

20. Outkast3r09

derp lol

21. Outkast3r09

@jim_thompson5910

22. Jemurray3

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

@jemurray3 so in other words i should do d1 d2 d3 partials and t1 t2 t3 partials

24. Jemurray3

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.