Question 54072
The period of a simple pendulum is directly proportional to the square root of its length. 
This means Period = ksqrt(length)
You need to find "k".
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If a pendulum has a length of 6 feet and a period of 2 seconds
This means 2=ksqrt6
Then k=2/sqrt6
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So now we know the formula for a perdulum is:
P=(2/sqrt6)sqrt(length)
P=2sqrt(length/6)
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To what length should it be shortened to achieve a 1 second period?
Using that formula you get:
1=2sqrt(length/6)
sqrt(length/6)=1/2
Square both sides to get:
(length/6)=1/4
length = 3/2 ft
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Cheers,
Stan H.