Final answer:
The function modeling the simple harmonic motion with an amplitude of 1.2 m and frequency of 0.5 Hz is x(t) = 1.2 cos(πt), with the angular frequency calculated as π rad/s.
Step-by-step explanation:
The task is to find a function that models the simple harmonic motion (SHM) with an amplitude of 1.2 meters and a frequency of 0.5 Hz. Since there is zero displacement at t=0, the cosine function is the appropriate choice for the displacement function. The general form of the displacement equation in SHM is x(t) = A cos(ωt + φ), where A is the amplitude, ω is the angular frequency, t is the time, and φ is the phase constant. Since displacement is zero at t=0, the phase constant can be considered 0 (zero phase shift).
First, find the angular frequency using the relationship ω = 2πf. With a frequency (f) of 0.5 Hz, ω = 2π(0.5 Hz) = π rad/s. The displacement function x(t) for this SHM can be expressed as x(t) = 1.2 cos(πt).