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19 March, 20:55

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.

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  1. 20 March, 00:18
    0
    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.
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