Expert: Richard J. Raridon - 5/9/2009

Question
QUESTION: 104. Time to swing. The period T (time in seconds for one complete
cycle) of a simple pendulum is related to the length L
(in feet) of the pendulum by the formula 8T2 = pi2L. If a
child is on a swing with a 10-foot chain, then how long
does it take to complete one cycle of the swing?

ANSWER: So just put in L=10 and calculate T to get 3.51s

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QUESTION: The formula is: 8T^2=pi^2L So is that still correct?  Thank you for your time.

Answer
Well, the standard way to write it is T = 2(pi)(L/g)^1/2 where g is the acceleration due to gravity.  In the metric system that's 9.8m/s^2 and in the English system 32.15ft/s^2.  So using 32 instead of 32.15 (only a slight error), then you get 8T^2 = (pi^2)L