# Errors in experimantal physics- how to combine st err of mean and apparatus uncertai.

#### trelek2

Hi all!

I'm currently doing an experiment using a compound pendulum trying to determine the value of g.

I have a problem with my uncertainties:

Error in period T:
The period is measured with the use of a photo-gate of accuracy +/- 0.0001s.
For each height i did 20 measurements from which i calculated average period and from the standard deviation I have the standard error of mean. However due to the fact that I made so many measurements the standard error of mean sometimes appears to be smaller than the actual precision of the photo-gate (for example +/- 0.00007s). What should I do in this case? I'm guessing I somehow need to combine these uncertainties?

I have another question concerning the heights.
I firstly had to measure the length of the whole pendulum to find the centre of mass being in the middle. Then I mark the center of mass and measure different heights up to the edge of clamp (this all using a meter stick). Then I measure the distance between edge of clamp and axis of rotation using vernier caliper.
Overall I guess it goes like this (correct me if I'm wrong)
Uncertainty of meter stick (with the help of magnifying glass) is 1/3mm so +/- 0,3mm.
And since I use this uncertainty twice (not sure if center of mass is exactly where marked) AND then when measuring distance to edge of clamp -this gives me +/- 0,6mm and I need to combine this with the uncertainty in the distance on clamp which is +/-0,05mm. So it is sqrt(0,6^2+0,05^2)?
Thank you in advance for all the help.
PS. If you're not sure please don't reply as I don't want to get more confused than I am.

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#### Dale

Mentor
Re: Errors in experimantal physics- how to combine st err of mean and apparatus uncer

Using the propagation of errors you have $$\sigma _g^2=\frac{16 \pi ^4 \sigma _L^2}{T^4}+\frac{64 L^2 \pi ^4 \sigma _T^2}{T^6}$$ where all of the sigma terms are standard deviations, not standard errors.

#### trelek2

Re: Errors in experimantal physics- how to combine st err of mean and apparatus uncer

Using the propagation of errors you have $$\sigma _g^2=\frac{16 \pi ^4 \sigma _L^2}{T^4}+\frac{64 L^2 \pi ^4 \sigma _T^2}{T^6}$$ where all of the sigma terms are standard deviations, not standard errors.
Sorry, but I don't understand how this helps me. I thought I explained what I'm doing quite clearly. I need to know what my error for the periods and heights will be.