Hey, so my lab instructor has decided he wants us to calculate propagated error on our lab reports now. Of course, none of us in the class have ANY clue how to do this because partial derivatives are not taught until the end of calc 2 (only calc 1 is a pre-req for this class). So, I need help trying to figure this out.
Can anyone explain how to find propagated error to me?
I mean, it kind of helps but I have a hard time knowing what numbers to put where. I might just be over complicating it. Here is the question:
In your report, comment on how the mass of the pulley influenced your results. If your graph does not pass through the origin, can you explain why? Calculate g from Equation 6.3 and a propagated error estimation using one of your larger values of the transferred mass. Show clearly the partial derivatives and the final propagation formula used for the uncertainty.
- Are you suppose to determine the error because of the influence the mass of the pulley have on your recorder times?
- What are your graph consisted of (what are on your y-axis [force?] and x-axis [time?]).
- You're probably suppose to get the partial derivatives of the function consisting of your x and y axis variables from the graph you constructed (or did they give you some graph for something?).
Your standard deviation is obviously of your time, so time (x) will be your first variable. Get the standard dev of your other variable (force?)(y) and get the partial derivatives of this function (graph).
I'll quickly describe how partial derivatives work...A partial derivative (PD) of a function [u=f(x, y)] of several variables is its derivative with respect to one of those variables, with the others held constant.
Ex: x2y + 3xy4
fx(PD with respect to x): 2xy + 3y4
fy(PD with respect to y): x2 + 12xy3
Look I'm totally just guessing here, haven't heard of propagated errors before, so I can be totally wrong. This is real hard if I don't know the whole setup...better give me rep for this, was kinda tedious...
Can anyone explain how to find propagated error to me?
Also found this: Calculation of Probable Propagated Error
Don't know if this is what you're looking for...
In your report, comment on how the mass of the pulley influenced your results. If your graph does not pass through the origin, can you explain why? Calculate g from Equation 6.3 and a propagated error estimation using one of your larger values of the transferred mass. Show clearly the partial derivatives and the final propagation formula used for the uncertainty.
Mass Transferred(g):8
Trial 1 Time(s): 4.03
Trial 2: 4.03
Trial 3: 3.97
Trial 4: 3.95
Trial 5: 4
Trial 6: 3.95
Average Time: 3.988333
Standard Dev: 0.037103
Acceleration(m/s^2): 0.129127
Net Force(N): 0.158826
Ignore the first two parts of the question.
- What are your graph consisted of (what are on your y-axis [force?] and x-axis [time?]).
- You're probably suppose to get the partial derivatives of the function consisting of your x and y axis variables from the graph you constructed (or did they give you some graph for something?).
Your standard deviation is obviously of your time, so time (x) will be your first variable. Get the standard dev of your other variable (force?)(y) and get the partial derivatives of this function (graph).
I'll quickly describe how partial derivatives work...A partial derivative (PD) of a function [u=f(x, y)] of several variables is its derivative with respect to one of those variables, with the others held constant.
Ex: x2y + 3xy4
fx(PD with respect to x): 2xy + 3y4
fy(PD with respect to y): x2 + 12xy3
Uncertainty equation
Substitute:
du/dx = fx.
du/dy = fy.
sx = 0.037103.
sy = ?.
Look I'm totally just guessing here, haven't heard of propagated errors before, so I can be totally wrong. This is real hard if I don't know the whole setup...better give me rep for this, was kinda tedious...