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 46407: 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 period?

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
You can start by writing the equation of proportionality:
Where: P = period, L = Length, and k is the constant of proportionality.
We need to find the value of k. We can do this by substituting the given values of L (6 ft) and P (2 secs) into the above formula and solving for k.
Divide both sides by

Now the formula for the period is:

To answer your probem however, we need to solve this equation for L.
Multiply both sides by and divide by 2.
Now square both sides.
Simplify.

Now we can answer your problem. What should L be if P is to be 1 second.
Just substitute P = 1 into the above equation and solve for L.

ft.
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