Data for the hanging slinky
Spring 2023

measurements={2+5/8,5+1/8,7+3/8,9+3/4,12,14+1/4,16+5/8,18+5/8,20+5/8,22+1/2,24+1/2,26+1/8,27+7/8,29+3/4,31+1/2,33, 34+1/2,35+3/4,37+1/4,38+5/8,39+7/8,41+1/8,42+1/4, 43+1/4,44+1/4,45+1/4,46+1/8,46+7/8,47+5/8,48+1/4,48+7/8}

oludata={48+1/2,49,49.5,50,50+3/8,50+7/8,51,51+1/4};

Olu’s data overlaps mine.  This will be something for you to figure out.

sabrinadata={51+3/8,51+5/8}

If we have 42 measurements, then 51+5/8 is the last and forty-second.  If so, the thirty-seventh should be 51+3/8 with four intervening coil measurements.  
That is to say, Sabrina has made two measurements; one is the measurement of the very (lowest) end of the slinky.  The other is not the previous coil measurement, but there are five coils “bunched” at the end, and it is not easy/practical to measure the position of those coils.

mccuanstart=ListPlot[measurements]

Length[measurements]

oluunknown={{32,10},{33,10},{34,10},{35,10},{36,10}};
sabrinamod={{37,51+3/8},{42,51+5/8}};
sabrinamid={{38,51+3/8+1/20},{39,51+3/8+2/20},{40,51+3/8+3/20},{41,51+3/8+4/20}};

ListPlot[oluunknown,PlotStyle->Red]

ListPlot[sabrinamid,PlotStyle->Green]

Show[mccuanstart,ListPlot[oluunknown,PlotStyle->Red],ListPlot[sabrinamod],ListPlot[sabrinamid,PlotStyle->Green],PlotRange->All]

We need five points from among Olu’s data, and he has given us eight points.  Let’s start by seeing which one fits best for point 32.

oluvert={{30,48+1/2},{31,49},{32,49.5},{33,50},{34,50+3/8},{35,50+7/8},{36,51},{37,51+1/4}};

It seems to me, the first two of Olu’s points overlap my data, and the last one overlaps Sabrina’s top point.  

Note:  Olu’s last two measurements are (exactly) 1/8 inch lower then mine.  Two comments about this:  1/8” is practically the margin for error for our measurements, and it is rather likely the consistency here comes from differences in the visual perception of the two observers, i.e., probably I just hold my eye a little lower than Olu.  

Comparing Olu’s last point to Sabrina’s first point, we have Olu exactly 1/8” lower than Sabrina.   If we assume Sabrina measures like I do, then the natural correction would be to position the data points as I have done above and add 1/8” to all of Olu’s measurements.  As I’ve mentioned, however, 1/8” is almost negligible, so I’m going to leave it at this for the moment.

Show[mccuanstart,ListPlot[oluunknown,PlotStyle->Red],ListPlot[sabrinamod],ListPlot[sabrinamid,PlotStyle->Green],ListPlot[oluvert,PlotStyle->Black],PlotRange->All]

Let me see if I can obtain a unified set of data.

Append[measurements,oludata[[1]]]

ListPlot[Append[measurements,oludata[[1]]]]

olulast={48+1/2,49,49.5,50,50+3/8,50+7/8,51,51+1/8};

oluplus=Append[measurements,oludata[[1]]];

lastplus=Append[measurements,olulast[[1]]];

end=Show[ListPlot[measurements,PlotStyle->Green],ListPlot[Append[measurements,oludata[[1]]],PlotStyle->{Red,AbsolutePointSize[2]}],PlotRange->All]

Show[end,ListPlot[lastplus,PlotStyle->{Blue,AbsolutePointSize[2]}],PlotRange->All]

Something clearly looks strange with the last data point here.   This must have something to do with the overlap, but I will leave it to you to figure that out.  (I will do the same, but I haven’t done it yet.

Keep a couple things in mind:  (1)  The data may need to be critically evaluated to determine if any errors in measurement might have been made, or were made.  
(2) We can go back and attempt to verify and/or correct the data by measuring again.