Determining g with a Compound Pendulum: Issues with Uncertainties

AI Thread Summary
The discussion focuses on determining the value of g using a compound pendulum while addressing uncertainties in measurements. The user encounters issues with the standard error of the mean being smaller than the precision of the photo-gate, prompting questions about how to combine uncertainties effectively. Additionally, there is confusion regarding the measurement of heights and the propagation of errors, particularly in combining uncertainties from multiple measurements. The user seeks clarification on calculating the total uncertainty for both period and height measurements. Accurate error analysis is crucial for reliable results in the experiment.
trelek2
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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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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<br /> \sigma _T^2}{T^6} where all of the sigma terms are standard deviations, not standard errors.
 


DaleSpam said:
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<br /> \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.
 
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