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

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Question 44132This question is from textbook Algebra and Trigonometry with Analytic geometry
: 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 peroid? Ok my answer is 3 feet but the question seems to have more to it I think. Thanks for checking this answer. This question is from textbook Algebra and Trigonometry with Analytic geometry

Answer by adamchapman(301) About Me  (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.
period = T
length= L
T=k%2Asqrt%28L%29
where k is a constant of proportionality.
to work out what k is, rearrange the equation above:
k=T%2Fsqrt%28L%29
originally,
T=2
L=6
this gives
k=2%2Fsqrt%286%29
So now we can write
T=%282%2Fsqrt%286%29%29%2Asqrt%28L%29
we want T to be 1, so:
1=%282%2Fsqrt%286%29%29%2Asqrt%28L%29
sqrt%286%29%2F2=sqrt%28L%29
6%2F4=L
L=3/2 ft.
I hope this helps
P.S. I am trying to start up my own homework help website. I would be extremely grateful if you would e-mail me some feedback on the help you received to adam.chapman@student.manchester.ac.uk