- #1
voltaire101
- 3
- 0
Homework Statement
Measurements of the height h(t) of water in a harbor are recorded ,where h is measured in meters and t in hours.It was noted that the rise and fall of a tide is modeled by a sinusoidal function giving the height by : h(t)=a+bsin(kt+c).
(a) Obtain values of the parameters a,b,c and k if measurement started when the level is equal to the mean level of 2.5 meters and has an amplitude of 1.5 meters and a period of 12 hours.
b) Compute the rate of change of the water height.
c) Find the highest and lowest values of h and the times at which they are taken.
Homework Equations
The Attempt at a Solution
This is a very complex problem (I think). OK, I tried to solve it in many way but with no progress, finally the doctor said that he will give us a hint. So I wrote this hint and I found it was very far from my attempts to solve it.
So I will type the doctor's hints..
at t=0 the height was 2.5
every 12 hours there is an amplitude of 1.5 meters
He also wrote this: (I don't know why he chose four periods)
when t=0 h=2.5
when t=12 h=4
when t=24 h=5.5
when t=36 h=7
when t=0 2.5=a+bsin(c)
when t=12 4=a+bsin(12k+c)
when t=24 5.5=a+bsin(24kc)
when t=36 7=a+bsin(36k+c)
for the first period:
sin(c)=[itex]\frac{2.5-a}{b}[/itex]
for the second period:
sin(12k+c)=sin(12k)cos(c)+cos(12k)sin(c)
... At this point I lost reception.
