Re: Linearizing Graphs

[Ed Schweber <edschweb@IX.NETCOM.COM>]

John Cooper replied to my question about linearizing graphs:

>    There are often more ways than one to force a linearizing
> transformation; but, if you are after parameters of the fit, e.g. >slope,
intercept, etc., you have to include appropriate, different >weightings for
different fits to get consistent values.

   But often the connection with these parameters is more direct when we
plot the dependendent variable vs. a transformation of the independent
variable than when we plot a transformation of the dependent variable vs.
the independent variable. Yet, most textbooks still approach the issue by
transforming the dependent variable.

   Actually, the question goes back a few years when the father of one of
our students, a recently retired academic physicist, came in to help out
when one of our other physics teachers suddenly quit. He correct me for
telling students to graph pendulum data as period vs, square root of length
and said they should graph period squared vs. length.
> >    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?

>   ^^^^^ Hunh?

  The pattern of transforming the dependent variable.

Thanks for the input.

Ed