Question 62539: The period of a simple pendulum is directly proportional to the square root of its length. If a pendulum has a length of 6 feet and a period of 2 seconds, to what length should it be shortened to achieve a 1 second period.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The period of a simple pendulum is directly proportional to the square root of its length. If a pendulum has a length of 6 feet and a period of 2 seconds, to what length should it be shortened to achieve a 1 second period.
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P=ksqrt(L)
If L=6 and P=2 sec, then
2=ksqrt6
k=2/sqrt(6)
k is the constant of proportionality for this particular pendulum.
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Formula:
Period = (2/sqrt6)sqrt(L)
If P = 1 second, then
1=(2/sqrt6)sqrtL
sqrtL=(sqrt6/2)
L=[(sqrt6/2]^2
L=6/4=3/2 or 1.5 ft.
Cheers,
Stan H.
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