Question

Find a function that models the simple harmonic motion having the given properties. Assume that the displacement is at its maximum at time t=0. amplitude 6.25 in., frequency 60Hz

Answer 1

The function that models the simple harmonic motion with an amplitude of 6.25 inches and frequency of 60Hz is x(t) = 6.25 cos(120πt).

Step-by-step explanation:

The student is looking for a function that models the simple harmonic motion with given properties. Given an amplitude of 6.25 inches and a frequency of 60Hz, and knowing that the displacement is at its maximum at t=0, the appropriate function in the form of x(t) = A cos(2πft) can be used. Here, A is the amplitude and f is the frequency. Since the frequency is 60Hz, the angular frequency ω would be ω = 2πf = 2π(60).

Therefore, the function modeling the simple harmonic motion is x(t) = 6.25 cos(120πt).