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]

[Phys-L] Re: measuring the period of a pendulum



When we do the pendulum lab we do it before having looked at any periodic
motion (other than uniform circular). The basic pendulum is shown to the
lab and they are told they are charged with trying to figure out just what
the period depends on. As a full group then they decide what factors
should be considered. They come up with Length, Amplitude (angle of
swing), and Mass of the bob. Then we break into 5 groups. One group IS to
study the angle with a 1 meter pendulum. They do multiple sets of 3 swings
each. The other groups are told to keep their angle of swing in the 20
degree range. Another group does a range from 3 to 90 grams for the bob
held at 1 meter. A third group does .1 to 1.5 meters, a fourth, 1-3
meters, and a fifth 2 to 11 meters. They take their data--most counting 10
swings again at 20 degrees or less. Each group must work up their data,
produce a graph, and by the end of the period report on their results.
The angle group will show that the period is pretty much independent of the
angle of swing for less than 30 degrees but they will see a 10-15% rise in
the period of 30 to 90 degrees. The mass people, of course, see no effect.
What I especially like about breaking up the length groups is that the
medium and long range groups will see their data as being linear. The
short range data does suggest a curve, but only once all three regions are
combined is it very clear that the dependency IS NOT linear. The learning
point then is that one CAN be fooled if the collected data samples too
small a range of possible values.

From here we proceed to power-law fits and getting an equation for the
period versus length data, but we have this nagging problem about the angle
of swing data. Only later, once we study SHM and ultimately derive the
pendulum equation, do we see why we saw such variations of period versus
angle of swing.

For my liberal arts class, this whole exercise is run as a simulation of a
commercial research lab--Acme Physics Inc. They are the experimental wing.
Elsewhere we have a room with an infinite number of monkeys pounding on
computers who will ultimately come up with a theoretical equation. Of
course my Calc level class can derive the equation themselves. The main
thing is that we try to have fun with this while at the same time learning
something about timing techniques, for the gen-ed class we introduce the
power law fitting, and then there is that danger of choosing too narrow a
range for collecting data. With the collected length data from 4 different
lab sections (maybe 120-150 data points) we usually can get a 'g' in the
9.65 range.

Rick




[Original Message]
From: Brian Whatcott <betwys1@SBCGLOBAL.NET>
To: <PHYS-L@LISTS.NAU.EDU>
Date: 11/22/2005 9:03:48 PM
Subject: Re: measuring the period of a pendulum

Timing multiple cycles begs several questions, such as:
1) How does the period vary with amplitude?
(You KNOW it does!)
2) I can time multiple periods if I maintain the amplitude
but how does the amplitude stabilization affect the period ?
(You KNOW it does!)

Ah the delusory chase for precision...of what?

_______________________________________________
Phys-L mailing list
Phys-L@electron.physics.buffalo.edu
https://www.physics.buffalo.edu/mailman/listinfo/phys-l