Question

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.

Answer 1

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

Answer 2

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