Impact of a elastic string on pendulum

[pschilk]

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?

 

[haruspex]

the linear regression has a y intercept of -0.04

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.

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.