Question

The period 7 (in seconds) of a pendulum is given by T = 2pi√( L divided by 32) where L stands for the length (in feet) of the pendulum. If pi = 3.14, and the period is 12.56 seconds, what is the length?

The length of the pendulum is _____ feet.

Answer 1

128 feet

Explanation:

`t = 2\pi \sqrt{(l)/(32) }`

So now we will substitute the values of T and π into the equation.

`12.56 = 2 * 3.14 \sqrt{ (l)/(32) }`

`12.56 = 6.28 \sqrt{ (l)/(32) }`

Divide both sides by 6.28

`2 = \sqrt{ (l)/(32) }`

Square both sides.

`4 = (l)/(32)`

Multiply both sides by 32

`l = 4 * 32 \\ l = 128 \: feets`