Abuoy 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.

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) + C

where 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 = B

d = 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.

typically if you want , you would actually put questions here for us to you. but hey, that's just me. maybe someone will magically answer the questions for you without knowing what they are.

correct answers below: