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Math Help - Sinusoidal Functions Help! URGENT

  1. #1
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    Sinusoidal Functions Help! URGENT

    I am studying for a test, and this is the question. Very Very Urgent.

    At an ocean port, the water has a max depth of 4m above the mean level at 8 am, and the period is 12.4 h. Assuming that the relation between the depth of the water and time is a sinusoidal function, write an equation for the depth of the water at any time t.


    I am terrible at modeling these equations. Any tips ?
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    Use the sine equation asin(2pi(t-s)/p))+d
    Where
    a=amplitude
    s=phase shift
    p=period
    d=horizontal shift

    sorry the equation looks messy, but the / is supposed to be divided.

    so, y=4sin(2pi(t-8)/12.4)

    i beleive thats correct, but i don't have a book on hand...hope that helps
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  3. #3
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    Quote Originally Posted by xoKELLY View Post
    I am studying for a test, and this is the question. Very Very Urgent.

    At an ocean port, the water has a max depth of 4m above the mean level at 8 am, and the period is 12.4 h. Assuming that the relation between the depth of the water and time is a sinusoidal function, write an equation for the depth of the water at any time t.


    I am terrible at modeling these equations. Any tips ?
    It will depend on how t is defined and where the depth is measured from. If the depth is measured from the seabed then the mean level cannot be zero (why?).

    If you define time t as hours after 8 am (so that t = 0 at 8 am) and d as depth measured (in metres) from the seabed then the best that can be done is:

    d = 4 \sin\left( \frac{2 \pi}{12.4} \, t + \frac{\pi}{2}\right) + C where C is the mean level.
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