Find a model for simple harmonic motion of a spring with a 3 foot displacement,

36 inch amplitude and a period of 4 seconds.

Since the displacement is 3 ft (that is, the spring is at 3 foot at t=0),

use the equation d=acos(ωt))

36 inches=3 feet (keep in same units!)=amplitude=a

Period=2π/ω → 4 seconds=2π/ω →ω=2π/4=π/2

The model is d=3cos(π/2*t)