SOLUTION: I have another word problem I understand but I don't understand.... The period of a simple pendulum is directly proportional to the square root of its length. If a pendulum has

Question 65558: I have another word problem I understand but I don't understand....
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 period of 1 second?
I understand:
Pendulum directly proportional to square root of length
6 feet with a period of 2 seconds
I am trying to find the length to be shortened to make a period of 1 second.
I know I might be nuking this....
Found 2 solutions by stanbon, funmath:
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 period of 1 second?
--------
Period = k (sqrt(length)
You need to find k.
2 sec = k (sqrt 6)ft
k=2/sqrt6=0.8164965...
EQUATION: P=(0.8164965..)sqrt(length)
Let P=1 sec and solve for length, as follows:
1=(0.08164965)sqrt(length)
sqrt(length)=1.224745
length = 1.5 ft
Cheers,
Stan H.

Answer by funmath(2933) (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 period of 1 second?
:
Pendulum directly proportional to square root of length
:
6 feet with a period of 2 seconds
:
I am trying to find the length to be shortened to make a period of 1 second.
Let period be: T
Let length be: L
The constant of proportionality is: k
Then in math symbols, "the period is directly proportional to the square root of length" is:

Find k when T=2 and L=6

Now let T=1:

L=1.5 ft
Happy Calculating!!!

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