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.

Question

a)write an equation the describes the distance of the object from its mean position as a function if time.

Answer 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