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.

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

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