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Thread: Finding period, frequency and hor shift?

  1. #1
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    Finding period, frequency and hor shift?

    Hey folks,

    Here is the question that I am struggling with.

    I am riding a Ferris Wheel. My height h in feet above the ground at any time t (in seconds) can be modeled by the following equation:

    h=28sin((pi*t)/12 - pi/2) +30

    What is the period, frequency, and horizontal shift of this function. Also, what are the minimum and maximum heights above the ground?
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  2. #2
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    $\displaystyle
    h=28sin\left(\frac{\pi t}{12} - \frac{\pi}{2}\right) +30 \Rightarrow h=28sin\left(\frac{\pi }{12}(t-6)\right) +30
    $

    Now consider
    $\displaystyle h=28sin\left(\frac{\pi }{12}(t-6)\right) +30$

    max hight will be 28+30, min height will be -28+30.

    frequency = $\displaystyle \frac{2\pi}{\frac{\pi}{12}} = 24$
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  3. #3
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    Quote Originally Posted by pickslides View Post
    frequency = $\displaystyle \frac{2\pi}{\frac{\pi}{12}} = 24$
    $\displaystyle Period=\frac{2\pi}{\frac{\pi}{12}} = 24$

    $\displaystyle
    frequency = \frac{1}{Period}=\frac{1}{24}
    $

    Horizontal Shift = 6 units Right.
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  4. #4
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    Wouldn't the horizontal shift be $\displaystyle pi/24 $right? I factored out the $\displaystyle pi/12$ and and got $\displaystyle 28sin pi/12(x-(pi/24)) +30$

    So would it by $\displaystyle pi/24 $to the right?
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  5. #5
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    if you factored out $\displaystyle \frac{\pi}{12}$ then how can there be $\displaystyle \pi$ remaining in your horizontal shift component?
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  6. #6
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    If I exapnd what you have above I get this

    $\displaystyle \frac{\pi}{12}\left(x-\frac{\pi}{24}\right) = \frac{\pi x}{12}x-\frac{\pi^2}{288}$

    This is no where near what you started with.
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