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

Answer:

128 feet

Step-by-step explanation:

$t = 2\pi \sqrt{\frac{l}{32} }$

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

$12.56 = 2 \times 3.14 \sqrt{ \frac{l}{32} }$

$12.56 = 6.28 \sqrt{ \frac{l}{32} }$

Divide both sides by 6.28

$2 = \sqrt{ \frac{l}{32} }$

Square both sides.

$4 = \frac{l}{32}$

Multiply both sides by 32

$l = 4 \times 32 \\ l = 128 \: feets$