Object's speed is max when passing through 0 displacement.
Object's acceleration is max at either end of its oscillation, and these two times are 1/4 period apart.
y = A sin (wt)
v= Aw cos(wt)
a = - A (w^2) sin (wt)
v max = Aw
a max= -A w^2
These relations can give you w= 2 pi/ T
where T = period of oscillation.
