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    Period, Amplitude, Range, Y-intercept and Phase Shift

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    Develop the solutions for the following problems:

    1.) Graph the function y = -1 + 2sin(x + π) over a 2-period interval.
    a. What is it's period?
    b. What is its amplitude?
    c. What is it's range?
    d. What is the y-intercept of it's graph?
    e. what is it's phase shift?

    2.) The formula for the up and down motion of a weight on a spring set in motion is
    s(t) = a sin √k/m t

    If the spring constant k is 6, what mass m must be used to produce a period of 1 sec.
    Hint: period = 2л/w

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    Solution Preview

    a function f is periodic with period t if
    f(x + t) = f(x)
    for all values of x in the domain of f.

    Please see the attached figure..

    A. From the graph we can see that the funtion has the same value when x = 2pi, 4pi etc. But the least positive value for which such a ...

    Solution Summary

    Period, Amplitude, Range, Y-intercept and Phase Shift are calculated for a given trigonometric function. A formula for weighted spring is elucidated. All work is shown.