Impact of a elastic string on pendulum

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SUMMARY

The discussion centers on the impact of elastic strings on the oscillation period of a pendulum, specifically measured using a light gate. The experiment revealed a y-intercept of -0.04 and a slope of 4.0769 in the T² vs l graph, indicating a slight underestimation of the period and a calculated gravitational acceleration of 9.7 m/s² instead of the expected 9.8 m/s². Participants suggested that the elasticity of the string could cause minor stretching at the lowest point of the swing, but emphasized that small amplitude swings would likely minimize this effect.

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  • Understanding of pendulum mechanics and oscillation principles
  • Familiarity with linear regression analysis and graph interpretation
  • Knowledge of gravitational acceleration and its calculation
  • Basic concepts of elasticity and its effects on physical systems
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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.