- #1

happyparticle

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- TL;DR Summary
- How to calculate the propagation of uncertainty with some constants

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 uncertainty by a constant.

##\sigma= (1000 \cdot 5 \cdot 10^{-8}) \cdot 0.1 = ##

and then for the power

##\sigma= \frac{2 (5\cdot 10^{-6}) \cdot (\sqrt{\omega r c)}}{\omega r c}##

Where I'm using this formula ##\frac{\sigma_f}{f} = \frac{n \sigma_a}{a}##

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 uncertainty by a constant.

##\sigma= (1000 \cdot 5 \cdot 10^{-8}) \cdot 0.1 = ##

and then for the power

##\sigma= \frac{2 (5\cdot 10^{-6}) \cdot (\sqrt{\omega r c)}}{\omega r c}##

Where I'm using this formula ##\frac{\sigma_f}{f} = \frac{n \sigma_a}{a}##