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

Algebra ->  Proportions -> 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      Log On


   

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) 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. 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) 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. 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:
T=k%2Asqrt%28L%29
Find k when T=2 and L=6
2=k%2Asqrt%286%29
2%2Fsqrt%286%29=k%2Asqrt%286%29%2F%28sqrt%286%29%29
2%2Fsqrt%286%29=k
T=%282%2Fsqrt%286%29%29%2Asqrt%28L%29
Now let T=1:
1=%282%2Fsqrt%286%29%29%2Asqrt%28L%29
%28sqrt%286%29%2F2%29%2A%281%29=%28sqrt%286%29%2F2%29%2A%282%2Fsqrt%286%29%29%2Asqrt%28L%29
%28sqrt%286%29%2F2%29=sqrt%28L%29
%28sqrt%286%29%2F2%29%5E2=%28sqrt%28L%29%29%5E2
6%2F4=L
3%2F2=L
1.5=L
L=1.5 ft
Happy Calculating!!!