An object moves in simple harmonic motion with period 7 seconds and amplitude 5cm. At time t=0 seconds, its displacement d from rest is 0cm, and initially it moves in a positive direction.

Question

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

Answer 1

Since we know d = 0 when t = 0, a sine function would work nicely here
So we know a = 5
period = 2π/k
k = 2π/7

d = 5sin (2π/7 t)