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Math Help - Simple Harmonic Motion

  1. #1
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    Exclamation Simple Harmonic Motion

    Hey guys.
    How exactly do I do this question???
    The rise and fall in sea level due to tides can be modelled by simple harmonic motion. On a certian day, a channel is 10 m deep at 9 am when it is low tide and 16 m deep at 4 pm when it is high tide. if a ship needs 12 m of water to sail down a channel safely, at what times between 9 am and 9 pm can the ship pass through?.
    Last edited by UltraGirl; May 5th 2010 at 12:52 AM.
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  2. #2
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    Quote Originally Posted by UltraGirl View Post
    Hey guys.
    How exactly do I do this question???
    The rise and fall in sea level due to tides can be modelled by simple harmonic motion. On a certian day, a channel is 10 m deep at 9 am when it is low tide and 16 m deep at 4 pm when it is high tide. if a ship needs 12 m of water to sail down a channel safely, at what times between 9 am and 9 pm can the ship pass through?.
    Start by defining a clock time for t = 0 and then find a model for the depth. I suggest setting t = 0 at 9.00 am and using the model d = a \sin (bt) + c. Your job is to determine the values of a, b and c. Then solve d \geq 12 for t and convert your answer to clock times.
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  3. #3
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    Ummm so I've managed to find that the ship can sail beginning from 11.45 am but I dont get how to get 8.15 pm when the ship can no longer sail (from the answers)

    ive found that the equation of motion is x = 13 - 3 cos(pi/7 * t)

    and so i let x = 12 and derived t =- 7/pi * arccos(1/3) + 14n where n is an integer...
    Last edited by UltraGirl; May 5th 2010 at 02:12 AM.
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  4. #4
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    Quote Originally Posted by UltraGirl View Post
    Ummm so I've managed to find that the ship can sail beginning from 11.45 am but I dont get how to get 8.15 pm when the ship can no longer sail (from the answers)

    ive found that the equation of motion is x = 13 - 3 cos(pi/7 * t)

    and so i let x = 12 and derived t =- 7/pi * arccos(1/3) + 14n where n is an integer...
    Draw graph of x = 13 - 3 cos(pi/7 * t) and x = 12 on the same set of axes to see what's happening.

    Note that cosine is negative in the second quadrant and the third quadrant ....
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