Spring Oscillation: Find Greatest Speed of 0.5kg Block

[Leviticus 08]

Homework Statement

A 0.5 kg block attached to an ideal spring (k = 100 N/m) oscillates on a horizontal frictionless surface. When the spring is 12 cm shorter than its equilibrium length, the speed of the block is 1.5 m/s. What is the greatest speed of the block?

Homework Equations

The force becomes F(x) = m a - k x
The equilibrium position is x = m a / k

I don't know what else to use

The Attempt at a Solution

I don't really have all the work at my fingertips I left it at home(I'm at work now)
I'm not looking for a solid solution just somewhere to start

 

[rl.bhat]

The velocity of the block is given by
v =sqrt(k/m)*sqrt(A^2 - x^2) where x is the displacement from the equilibrium position.
Substitute the values and find the A.
For maximum velocity x = ...?