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9. Pendulum
Note that g 2 0.9940 m/s 2 which is within 0.6% of exactly 1 m/s 2 . Furthermore
g 2 0.9970 m1 2 /s or within 0.3% of exactly 1 m1 2 /s . The fractional error in the
approximation for T is
Tapprox Texact Tapprox
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2
2 seconds, increase the length of the pendulum by a factor of 4 to 1 m.
Now suppose that we have a pendulum driven clock with a mass at the end of a brass
bar. If the length of the bar is 1m then the period is 2s. (The half period is 1s.) The
coefficient of linear expansion of brass is brass 19 10 6 /C . For a change in
temperature T 10 C , the fractional change in the length of the pendulum is
L
brass T 1.9 10 4 . The fractional change in the period is
L
T
L
1
1 9.5 10 5 or 0.34 seconds/hour.
T
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12
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