A buoy floating in the ocean is bobbing in simple harmonic motion with period 7 seconds and amplitude 6ft. Its displacement d from sea level at time t=0 seconds is -6ft, and initially it moves upward. (Note that upward is the positive direction.)Give the equation modeling the displacement d as a function of time t.

Answer:d = 6 sin(2π/7 t + 3π/2)Step-by-step explanation:Equation for simple harmonic motion is:d = A sin(2π/T t + B) + Cwhere A is the amplitude,T is the period,B is the horizontal shift (phase shift),and C is the vertical shift.Given that A = 6, T = 7, and C = 0:d = 6 sin(2π/7 t + B)At t = 0, the buoy is at d = -6:-6 = 6 sin(2π/7 (0) + B)-1 = sin(B)3π/2 = Bd = 6 sin(2π/7 t + 3π/2)Notice you can also use cosine instead of sine and get a different phase shift.d = 6 cos(2π/7 t + π)You can even use phase shift properties to simplify:d = -6 cos(2π/7 t)Any of these answers are correct.