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Re: Linearizing Graphs



The choice between T^2 vs. L and T vs. Sqrt[L] is not really
arbitrary. While it might be easier (I'm not really sure of this) "for
students to understand" the latter, the former is overwhelmingly easier to
understand if one wishes to show a graphical meaning to uncertainties when
they are properly calculated. Estimation of the correlation or "goodness
of fit" as a function of the independent variable are equally obtuse when
that variable is Sqrt[L] rather than L.

To make all of this more clear, I prefer "inverting the equation" for T
vs. Sqrt[L] to the form which represents Sqrt[L] vs. T (simply swap axes).
Arguments re: Xi^2 (goodness of fit), correlation, etc. then follow the
standard prescriptions and interpretations.
(See Bevington, Taylor, etc.)

On Tue, 19 Oct 1999, Ed Schweber wrote:
Hi all:
This question refers to pendulums (or is it pendula?) as an example, but
is more general.
If we want to force a graph exeperimental data for period, T, of a
pendulum vs its length, L, into being a straight line we usually plot T^2
vs. L. But a graph of T vs sqrt(L) would also be linear and seems to be
easier for students to understand. Is there any reason besides convention
for doing it one way as opposed to the other?
When we linearize data for a discharging capacitor (potential, V, vs.
time, T) I can see an advantage to plottimg lnV vs. T rather than V vs
e^(-t). Is what we do with pendulums just a carry over of this pattern?
Thanks for any input.
Ed Schweber


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