Uncertainty propagation Definition and 17 Threads

I have seen that there are two different formulas that we can use when calculating the propagation of uncertainty in a measurement. If ##X=f(A, B, C, \ldots)## is the quantity whose uncertainty we want to estimate, which depends on the quantities ##A,B,C,...##, then we could calculate the...

Hi, I have a value ##100 \pm 0.1## and a function ##\frac{V}{E} = \frac{1}{\sqrt{1 + (\omega r c)^2}}## and I would like to find the uncertainty. Where r = 1000 and c = ##5 \cdot 10^{-8}## are constants. However, I'm not sure to understand how. Here's what I think and did. Since I multiply the...

Howdie! We have been playing around with melting and molding HDPE pellets recently. After that, we measured their diameter and thickiness 5 times each to get an uncertainty. In our experiments we put one pellet between gamma-source and detector and measure its attenuation. After that we place...

Hi! I was wondering how would I calculate the uncertainty of a value that is calculated using both multiplication and division? For example, with something like: Q = mc(T2 - T1) I'm not sure what to do with the uncertainties for T2 - T1 uncertainty = Δm/m + Δc/c + (ΔT1 + ΔT2)/(T1 + T2) Or...

So the only part of this question I am having an issue with is the uncertainty part in part e). I have included the whole question as reference. So to derive the uncertainty in ff I used the uncertainty equation outlined above but the issue is that when I propagate the uncertainty I end up with...

Homework Statement [/B] So basically I am calculating the terminal velocity for a small sphere falling in a measuring cylinder filled with glycerine. The distance traveled is 20 cm (0.20 m), and I have conducted 3 trials for each temperature. I have measured the displacement of the ball using...

Homework Statement Homework EquationsThe Attempt at a Solution The answer is different though,

I'd need to combine several vector-valued estimates of a physical quantity in order to obtain a better estimate with less uncertainty. As in the scalar case, the weighted mean of multiple estimates can provide a maximum likelihood estimate. For independent estimates we simply replace the...

Suppose I have some observables \alpha, \beta, \gamma whose central values and uncertainties \sigma_{\alpha}, \sigma_{\beta}, \sigma_{\gamma} are known. Define a function f(\alpha, \beta, \gamma) which has both real and complex parts. How do I do standard error propagation when imaginary...

I am a senior physics and mathematics major, and this is my last semester. As a result, I am taking advanced physics lab, which feels more like a grad school experiment than an undergrad. One of the labs deals with the modal analysis of three spring-mass systems placed vertically as shown in the...

Hi, I'm looking at an Italian high-school physics textbook. The subject is uncertainty propagation, and the target is 9th grade students. The book is allegedly by J.S. Walker, but I'm not sure how much it was "redacted" by the Italian editor. I am a little puzzled by two rules that are stated...

Say I have a 0-10 lbf load cell that can measure the force it takes to lift an object. The load cell is accurate to 1% of the full scale. I take 5 measurements and get the following readings: 5.2, 5.1, 4.9, 5.0, & 4.8, all in lbf. Now I am asked to give the mean with the associated...

Hi guys, So I'm writing up a physics lab and I have a bunch of data points. All of these data points have both x and y error bars. The relationship between x and y is linear and so I've made a line of best fit using Python passing through the data. Now the slope of that line of best fit...

I am measuring an average signal through a range of filters and compute the standard deviation of that signal over a certain range on my image plate. Now I want to normalise all of the signals to an arbitrary filter signal - does the standard equation of uncertainty propagation hold...

A while back, one of my undergraduate physics professors gave an argument for why the uncertainty in a function or quantity F is given by \Delta F = \sqrt{^{N}_{i-1}\sum(\frac{\partial F}{\partial x_{i}})^{2}(\Delta x_{i})^{2}} He argued to think of a right triangle and think of...

Homework Statement I have conducted an experiment which attempts to calculate the range of the visible light spectrum. Basically white light was shined through a diffraction grating (300 lines/mm) and diffraction theory is applied to calculate the wavelength. So, here are the variables...

Homework Statement Calculate "f" and its uncertainty, watch the units, show all work. Homework Equations f(x,z)= z/x x=100.5(+ or -) 3.8 cm y=71(+ or -) 1 s The Attempt at a Solution ok so i know that to find uncertainty i have to use the equation delta f(x,y)=df(x,y)/dx...