# Thread: Sinusoidal Functions Help! URGENT

1. ## 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 ?

2. 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

3. Originally Posted by xoKELLY
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:

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