Impact of a elastic string on pendulum

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The discussion revolves around the impact of elastic string on the oscillation period of a pendulum. The experiment revealed that the elastic nature of the string caused slight deviations in the recorded periods, leading to a y-intercept of -0.04 and a slope of 4.0769, which suggests an inaccurate gravitational constant of 9.7 m/s² instead of the expected 9.8 m/s². Participants noted that the elasticity might stretch the cord at the lowest point but deemed it unlikely to be a significant source of error due to the small amplitude of swings. Suggestions included analyzing the data points for systematic errors and considering the elasticity's impact in relation to other error sources. Overall, understanding the effects of string elasticity is crucial for accurate pendulum measurements.
pschilk
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Hello All,

I was performing an experiment in which the perod of oscllation of a pendulun at different lengths is measured using a light gate.

while performing the experiment i noticed that the string was slightly elastic, differing from the perfect pendulum.

I was attempting to figure outwhat kind of impact this may have had.

On my T^2 (s^2) vs l (m) graph the errors I could identify where the folliwng:

the linear regression has a y intercept of -0.04. Small but present. So all Periods where recorded slightly too low or all lengrhs slightly to small

the slope is slightly to high at 4.0769, which yields a value gor g of around 9.7 ms^-2 instead of 9.8. Perfect slope would be 4.028

And ofc there was some random error on each data point.

But i am not able to research how a slight elasticity in the cord would affect the results. Any ideas?
 
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pschilk said:
the linear regression has a y intercept of -0.04
pschilk said:
the slope is slightly to high
If you force the line to go through the origin (add a lot of (0,0) datapoints) does the slope look better? If so, what does that tell you about which datapoints are the problem?
If you look at the general scatter of the datapoints about the line, could the error in the slope just be happenstance rather than a systematic error?
See if http://pages.mtu.edu/~fmorriso/cm3215/UncertaintySlopeInterceptOfLeastSquaresFit.pdf helps.
pschilk said:
how a slight elasticity in the cord would affect the results.
It would slightly stretch the cord at the lowest point because of the centripetal force needed, but you should be using small amplitude swings, so I think it unlikely to be much of a source of error. If you know the elasticity you could calculate a limit on the error from that. You would nee to compare that with other error sources.
 

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