Simple Harmonic Motion Question (Springs)

[LucasCammarata]

A 350-g mass is attached to a spring whose spring constant is 64 N/m. Its maximum acceleration is 5.3 m/s2. What is its maximum speed?

So, i had a go at the question which basically required the knowledge that maximum acceleration occurs when displacement is maximum and maximum velocity occurs when displacement is zero.

So, i used the formula that acceleration = -w^2 [x(t)]... getting the result that... 5.3 = -w^2[x(t)] and solved for x(t) using the fact that w^2 = k/m.. therefore getting that maximum displacement = 0.028984375m. Does anyone know where i can go from here to get the maximum speed?

 

[AlephNumbers]

There is a relation between the spring energy when the mass is at its maximum displacement, and the kinetic energy of the mass when the spring is not exerting a force on the mass. Use this.