Final answer:
To find the period of a pendulum, use the formula T = 2π√(L/g). After converting the pendulum length from feet to meters, the calculated period does not match the options given, suggesting a possible error in the question. Once the period is known, the equation for the motion of the pendulum can be written in the form y = Acos(ωt).
Step-by-step explanation:
The student's question revolves around finding the period of a pendulum and its corresponding equation in cosine form. The period of a simple pendulum depends on its length and the acceleration due to gravity, and it can be approximated (for small amplitudes) by the formula T = 2π√(L/g), where T is the period, L is the length, and g is the acceleration due to gravity, typically 9.81 m/s2 on Earth. Since the pendulum length is given in feet, we need to convert it to meters first (1 foot = 0.3048 meter).
Let's calculate the period using the provided pendulum length of 3.5 feet, which is approximately 1.067 meters:
T = 2π√(1.067 meters / 9.81 m/s2)
T ≈ 2.07 seconds
This period does not perfectly match any of the options provided in the question, but it appears there may be a mistake in the set options. Regardless, once we have the correct period, we could determine the angular frequency ω using the formula ω = 2π/T, and then write the equation for the pendulum's motion as y = Acos(ωt), where A is the amplitude.