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

1. anonymous

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

2. anonymous

@JenniferSmart1 @jim_thompson5910

3. anonymous

for what class is this?

4. anonymous

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

5. anonymous

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

6. anonymous

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

7. anonymous

@Jemurray3

8. anonymous

@TuringTest

9. anonymous

@JamesJ

10. anonymous

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

11. anonymous

|dw:1360620861233:dw|

12. anonymous

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

13. anonymous

using partials of course

14. anonymous

|dw:1360620933162:dw|

15. anonymous

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. anonymous

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

17. anonymous

any luck turing?

18. anonymous

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. anonymous

derp lol

21. anonymous

@jim_thompson5910

22. anonymous

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. anonymous

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

24. anonymous

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.