trig

An object suspended from a spring is oscillating up and down. The distance from the high point to the low point is 30 cm, and the objects take 4 sec to complete 5 cycles.For the first few cycles the distance from the mean position, d(t), in cm with respect to the time t sec is modeled by a sin function.
a)write an equation the describes the distance of the object from its mean position as a function if time.

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  1. general shape
    d = a sin kt

    we know a = 15
    and if it takes 4 sec to complete 5 cycles
    then 1 cycle or 1 period = 4/5 seconds

    to find k,
    2π/k= 4/5
    4k = 10π
    k = 5π/2

    equation:
    d = 15 sin (5π/2) t

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