Math Help Forum - View Single Post

Jhevon · #2 October 10th, 2007, 02:50 PM

Quote:

Originally Posted by steve@thecostins.co.uk

In a small harbour, the depth of the water at high tide is 10m, and at low tide is exactly zero. The depth of water follows approximately simple harmonic motion with amplitude (A), 5m and time period (T), 12 hours. On one day, high tide is noon.

If d is the depth of the water above the mean depth (5m), write an equation of the form $d = A \ {\cos {\omega}t}$ , substituting the appropriate values for $A$ and ${\omega}$ .

Where, $t$ is time.

I already know $A = 5$ and ${\omega} = 0.5 \ rad \ h^{-1}$ or ${\omega} = 1.45 \ rad \ s^{-1}$ but i am not sure what the question is asking me to do. Does it want me to make a function for time so that when you input a time of day it will return an appropriate value? I am not sure, any ideas anyone?

Thanks

they just want you to rewrite the formula with your values substituted.

how did you find $\omega$ ? perhaps i don't know how to deal with simple harmonic motion, but since the period is 12, i'd say $\omega = \frac {\pi}6$

so the answer using my values would be: $d = 5 \cos \frac {\pi t}6$