How do i develop an equation for this function?

Question

A mass is supported by a spring so that it is at rest 0.5 m above a tabletop. The mass is pulled down 0.4 m and released at time t = 0, creating a periodic up and down motion that can be modelled using a trigonometric function. It takes 1.2 seconds to return to the lowest position each time.

Answer 1

I redid this post, I remember now.

The equation is

x = Acos(ωt + Φ)

A is the amplitude

ω is the angular velocity, 2πf, or sqrt(k/m)

Φ is the phase shift, if there is no displacement then it is π/2.

Also, this can be written a bit easier (if it starts at zero) with a sine function, as everything else would be the same except it would be x=Asin(ωt + 0), since sin(0) = 0

to get velocity or acceleration, just differenciate x(t)