SOLUTION: 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

Question 78467: 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 1 second period?
a. 1 foot
b. 1.5 foot
c. 2 feet
d. 3 feet
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
We have the equation
"The period of a simple pendulum is directly proportional to the square root of its length"
Substitute L=6 and T=2 and solve for k

Divide both sides by
So our constant is

Now the equation becomes

Now plug in T=1 to solve for L

Divide both sides by
Divide
Square both sides

reduce
So our length must be 1.5 feet to have a period of 1 second.

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