An object moves in simple harmonic motion with period 6 minutes and amplitude 13 . At time t=0 minutes, its displacement d from rest is -13m , and initially it moves in a positive direction.

Question

Give the equation modeling the displacement d as a function of time t.

Answer 1

Midline will be at -13 which is your vertical shift(d)

Amplitude (a) -s 13 si will move up to 0, back to midline(-13), down to -26 and then back to midline to complete the cycle. This would conform to a sine graph

There is no phase shift

Period is 6 minutes so b= 2pi/6 or pi/3

Equation therefor is y= 13sin[(pi/3)x] -13