Final answer:
The formula for the period T of a pendulum is given by the relation T = 2π√(L/g). For the provided scenario, where g is 32 feet/second², the correct equation representing the period of a simple pendulum is A) T = 2√(L/32).
Step-by-step explanation:
Determining the Correct Pendulum Period Equation
The formula for the period T of a simple pendulum depends on its length L and the acceleration due to gravity g. Given that the time a pendulum takes to move back and forth once is 2 times the square root of the length of the pendulum L, in feet, divided by the square root of the acceleration due to gravity, which is 32 feet/second², we can identify the correct equation from the provided options.
The standard formula for the period of a simple pendulum in simple harmonic motion, assuming the angle of deflection is less than 15 degrees, is T = 2π√(L/g). To find g, we would rearrange the equation to solve for g given a known period and length. However, this is not necessary for this question as we are only verifying the formula as it relates to length L and gravity.
Looking at the options, the correct one that represents the period of a simple pendulum is A) T = 2√(L/32) because it shows the period T as 2 times the square root of the length of the pendulum divided by the square root of 32, consistent with the given physical concept of pendulum motion and the formula derived from simple harmonic motion principles.