Question

An object attached to a horizontal spring is oscillating back and forth along a frictionless surface. The maximum speed of the object is 1.15 m/s, and its maximum acceleration is 6.52 m/s2. How much time elapses between an instant when the object's speed is at a maximum and the next instant when its acceleration is at a maximum?

Answer 1

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.