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College Algebra & Trigonometry

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A weight is attached to an elastic spring that is suspended from a ceiling. If the weight is pulled 1 inch below its rest position and released its displacement in inches after t seconds is given by x(t)=2cos(5ðt+ð/3). Find the first two times for which the displacement s 1.5 inches.

  • College Algebra & Trigonometry - ,

    what's the problem? You have the formula:

    x(t) = 2cos(5pi t + pi/3)
    just solve

    2cos(5pi t + pi/3) = 3/2
    cos(5pi t + pi/3) = 3/4

    cos .722 = .75

    so,
    5pi t + pi/3 = .722 or 2pi-.722=5.560
    t = (.722-pi/3)/5pi = -.021 or 6.262
    t = (5.560-pi/3)/5pi = .287

    see the graph at

    http://www.wolframalpha.com/input/?i=solve+2cos%285pi+t+%2B+pi%2F3%29+%3D+3%2F2

    You need to find the next occurrence after 0.287 by noting that the period is 0.4

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