PHY 241
University Physics
Experiment 9
The Simple Pendulum
Jacob Matson
Lab Partner:
Chip Pitkin
Performed: Mar 23 2006
Submitted: Mar 30 2006
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View Full DocumentObjective:
To study the parameters affecting the period of a simple
pendulum and to use a simple pendulum to determine the acceleration of
gravity.
Apparatus:
Pendulum clamp and support, metallic pendulum bob, dual
cords, photogate timer apparatus with computer interface, meter stick with
caliper jaws.
Theory:
A simple pendulum is defined as a point mass attached to a
massless cord. The period of a simple pendulum is determined by three
factors, its amplitude, its length, and the acceleration of gravity. If the
amplitude of motion is very small, its period is given by equation 1.
When the amplitude is large, the period increases with amplitude in a way
that can be approximated by a taylor series expansion as given by equation
2.
With this modification, the period of a simple pendulum can be estimated to
a fraction of one percent even with an amplitude of 90 degrees. If equation 2
is solved for the acceleration of gravity the resulting formula is equation 3.
In fact, for relatively small amplitudes, equation 3 can yield extremely
accurate values for the acceleration of gravity (if the mass is small but dense,
and if all the sources of friction and air resistance are kept minimal).
Experimentally, it is easier to get accurate measurements of the horizontal
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 Spring '06
 Puntenney
 Physics, Jacob Matson

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