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Sinusoidal function, find its parameters

  1. Dec 11, 2011 #1
    1. The problem statement, all variables and given/known data

    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.


    2. Relevant equations



    3. 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.
     
  2. jcsd
  3. Dec 12, 2011 #2
    Does this get you started?
     

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