The period T in seconds of a simple pendulum of length L in feet is given by T=2π√L/32. Determine the length in feet of a simple pendulum whose period is 8.72 seconds. Round your answer to the nearest foot.

1972 feet.

387 feet.

62 feet.

256 feet.

In this situation, you have to use the equation

T = 2π√L / 32

We need to find L so we have:

T / 2π = √L / 32

(T / 2π) ^ 2 = L / 32

L = 32 * (T / 2π) ^ 2

Substitute the values:

L = 32 * (8.72 / (2 * (3.14))) ^ 2

L = 61.69694511 feet

L = 62 feet

So the Answer is

L = 62 feet

For this case we have the following equation:

T = 2π√L / 32

Clearing L we have:

T / 2π = √L / 32

(T / 2π) ^ 2 = L / 32

L = 32 * (T / 2π) ^ 2

Substituting values:

L = 32 * (8.72 / (2 * (3.14))) ^ 2

L = 61.69694511 feet

Round to the nearest foot:

L = 62 feet

Answer:

L = 62 feet