Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: Linearizing Graphs



I've been following this discussion with some interest, as I have my own
opinions on the matter (don't we all?).

My experience has been that every time you do something to the basic
parameters like pendulum period, or pendulum length, you lose a few students.
As a result I tend to plot first the basic parameters, and then superimpose a
model function of the appropriate shape. The model function parameters can be
fit either by manual adjustment or by an automatic curve fit. Any physical
parameters desired can be extracted from the model. There is no essential
reason that the graph must be linearized, so why lose students along the way?

Time and student skill permitting, I then might move on to have students plot
something like T^2 vs. length, in the case of the pendulum lab. This step is a
good but not essential extension to the lab.

To some extent, the whole idea of linearizing a graph is a hold-over from the
pre-computer days. At that time, one had to come up with a way of making the
graph linear (using transformations, log-log, or semi-log paper) so one could
extract a slope. With easy computer graphing, we can now plot the basic
information and superimpose the appropriate model as needed, so the
linearization (and the accompanying distortion of fitting weights, which has
been mentioned but must be repeated here) is not needed.

There is still a reason to linearize graphs--it is much easier by eye to
recognize a straight line than a square root function. If you're fishing for
the relationship, then linearization is useful. If you know the relationship a
priori, then it is not so critical.

A couple of specific questions follow below, inserted in Ed's comments:

<-----Original Message-----

<[mailto:PHYS-L@lists.nau.edu]On Behalf Of Ed Schweber
<Sent: Wednesday, October 20, 1999 6:54 AM

< But often the connection with these parameters is more direct when we
<plot the dependent 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.
<

I don't understand. "Connection with these variables"? Does that mean that the
slope of a line might be proportional to 1/g, rather than the square root of
same? Does that matter at all, since you still have to do some algebra to
extract a value? I don't see that it makes any difference.


< 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.

Again, I don't see that either method of graphing is wrong or right. Both are
ways of graphing the data that illuminate the relationship. Either is fine,
but both add a level of complexity that is not essential to understanding the
experiment. Helpful, yes, but not essential.

JEG

__________________________________

John E. Gastineau john@gastineau.org
953 National Road, #163 (304) 243-9636 voice
Wheeling WV 26003-6440 (304) 243-9637 fax
USA http://gastineau.home.mindspring.com