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Math Help - Find equation for trig word problem

  1. #1
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    Find equation for trig word problem

    the word problem is:

    A mass is supported by a spring so that it is at rest 0.5 m above a tabletop. The mass is pulled down 0.4 m and released at time t = 0, creating a periodic up and down motion that can be modelled using a trigonometric function. It takes 1.2 seconds to return to the lowest position each time.

    so i know it will be a sin(x) graph, and i know it starts 0.5m above ground level, therefore the vertical shift is 0.5m - that will give us:
    y = a sin (x) + 0.5
    the mass will be pulled down 0.4, and will rise 0.4 above where it was stationary (so 0.4m + 0.5m = 0.9m is the maximum). I can determine the amplitude: (0.9 - 0.8)/2 = 0.4, so that will give us:
    y = 0.4 sin (x) + 0.5
    the only two things i'm not sure about is the phase shift and the horizontal stretch.
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  2. #2
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    Quote Originally Posted by snypeshow View Post
    It takes 1.2 seconds to return to the lowest position each time.

    y = 0.4 sin (x) + 0.5
    the only two things i'm not sure about is the phase shift and the horizontal stretch.
    for the horizontal stretch consider

    y = 0.4 \sin (nx) + 0.5 where 1.2 = \frac{2\pi}{n}


    for the phase shift think about the following. The sine wave needs to be shifted so it starts at a min.

    alter the model to be

    y = 0.4 \sin (n(x-b)) + 0.5 where b is the vertical shift.
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  3. #3
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    n = 5/3pi

    but i don't understand how i would get b

    EDIT: would the final equation be:

    y = 0.4 sin (5/3pi [x-3/10]) + 0.5

    because it's moved 3/10pi units?
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  4. #4
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    The min value on the sine wave occurs exactly 3 quarters of the way through the length of 1.2 seconds. What is 3 quarters of 1.2?
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    9/10? so the equation would be:

    y = 0.4 sin (5/3pi [x-9/10]) + 0.5

    i'm not sure if it's -9/10 or +9/10

    but the standard form for the equation is y = a trig [ n ( x - h) ] + k

    so since it's 9/10 (positive, not negative), and pos * neg = neg, i'm guessing it's:

    y = 0.4 sin (5/3pi [x-9/10]) + 0.5

    right?

    EDIT: I just graphed it and found out it's +10 because it's moving right. thanks for your help!!
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    Quote Originally Posted by pickslides View Post
    What is 3 quarters of 1.2?
    I think its 0.9

    \frac{3}{4}\times 1.2= \frac{3\times 1.2}{4} = \frac{3.6}{4}=0.9
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  7. #7
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    36/40 = 9/10
    9/10 = 0.9
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  8. #8
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    Quote Originally Posted by snypeshow View Post
    36/40 = 9/10
    9/10 = 0.9
    Totally mis-read what you wrote!
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