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Math Help - Modelling Sinusoidal Equations

  1. #1
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    Modelling Sinusoidal Equations

    I figured that making a post asking how to do this would be a lot better than posting a bunch of different questions. I am having trouble setting up word problems that are given to me, such as

    "A certain mass is supported by a spring so that it is at rest 0.5 m above a table top. The mass is pulled down 0.4 m and realeased at time t=0, creating a periodic up and down motion, called simple harmoic motion. It takes 1.2s for the mass to return to the low position each time. Draw a graphing shwing the height of the mass above the table top as a function for the first 2.0s. Write an equation for this function"

    or

    "A ferris wheel has a radius of 25 m, and its centre is 26 m above the ground. It rotates once every 50 s. Suppose you get on at the bottom at t=0. Draw a graph showing how your height above the ground changes during the first two minutes. Write an equation for this function"

    I can graph the equation, Im just absolutely terrible at setting them up. Can anyone explain step by step? Thanks.
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  2. #2
    Super Member Aryth's Avatar
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    Quote Originally Posted by xoKELLY View Post
    I figured that making a post asking how to do this would be a lot better than posting a bunch of different questions. I am having trouble setting up word problems that are given to me, such as

    "A certain mass is supported by a spring so that it is at rest 0.5 m above a table top. The mass is pulled down 0.4 m and realeased at time t=0, creating a periodic up and down motion, called simple harmoic motion. It takes 1.2s for the mass to return to the low position each time. Draw a graphing shwing the height of the mass above the table top as a function for the first 2.0s. Write an equation for this function"

    or

    "A ferris wheel has a radius of 25 m, and its centre is 26 m above the ground. It rotates once every 50 s. Suppose you get on at the bottom at t=0. Draw a graph showing how your height above the ground changes during the first two minutes. Write an equation for this function"

    I can graph the equation, Im just absolutely terrible at setting them up. Can anyone explain step by step? Thanks.
    I can do the second one for you.

    The general form of the sine function is:

    y = \alpha\sin{(\omega t + \phi)}

    The phase angle \phi is \frac{\pi}{2} since it starts at the maximum depth.

    \alpha is the amplitude, which in this case is 25m.

    \omega is the angular frequency, represented by:

    \omega = 2 \pi f

    f is the frequency of the wave, represented by:

    f = \frac{1}{T}

    T is the period, which in this case is 50s.

    So, we have:

    \omega = \frac{\pi}{25}

    So, the equation is:

    y = 25\sin{\left(\frac{\pi}{25}t + \frac{\pi}{2}\right)}

    To verify:

    y = 25 \sin{\left(\frac{\pi}{25}(100) + \frac{\pi}{2}\right)}

    y = 25 \sin{\left(4\pi + \frac{\pi}{2}\right)}

    y = 25 \sin{\left(\frac{9\pi}{2}\right)}

    y = 25m

    And there ya go.
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