Evaluate when pendulum data fit the simple harmonic model by separating large-angle restoring-force deviations from measurement errors.
10 points; suggested time: 25-30 minutes A group of students are given the following supplies: a stopwatch, a long string, various metersticks and protractors, and a large supply of various styles of predetermined masses.
What are the common sources of error or expected deviations from ideal results that might happen during this investigation?
Which of the three investigations might you expect to deviate the most from the ideal results and why?
(c) 1 point. Beyond the usual random errors of measurement (especially
when using a timer but minimized by taking the median value of a
few trials each time), one predictable deviation is in the amplitude
investigation. Pendulums actually behave as simple harmonic
oscillators only under the conditions of small angles (small enough
that sinθ is approximately θ). A large enough amplitude will
require the pendulum to oscillate at larger angles. This means that at
large amplitudes, one can predict the results to deviate from the
expected as the gravitational force no longer acts as a simple
restorative force.
One other possible source of systematic error would be in the mass
investigation. As various masses are swapped out on a fixed length
of string, the students may inadvertently be changing the length of
the string when adding different-sized masses. The length of the
pendulum is from the pivot point to the center of mass. If the
students do not compensate for this by shortening the string when
adding larger masses, they may see an artificial relationship at
higher masses in their graph of mass versus period.