The wording of this problem is a little tricky. The word "push" is used, and it probably makes you think "push"="force". Instead, you should think of this as an initial value problem (IVP) with an initial velocity undergoing free vibration.
So, draw your FBD and you'll get:
mx'' + kx = 0, with x(0)=0 and x'(0)=v0=1.5 m/s
Let me know if you need more help from there.