How do I find the time of a bullet embedded into a block on a spring?

[agentlee]

Homework Statement

A 2.25g bullet embeds itsself in a 1.50kg block, which is attached to a spring of force constant 785N/m. If the max compression of the spring is 5.88cm, find the initial speed of the bullet and the time for the bullet block system to come to rest.

The speed comes out to be 897.43m/s

Homework Equations

mvi=mvf
1/2mv^2=1/2kx^2
T=2∏√m/k

The Attempt at a Solution

I was able to find the initial speed of the bullet and only got stuck on the second part. I thought that since I'm given the distance and I found the speed of the bullet and block system, I could divide them to get the time.
The other time equation did not work either. Please help!

 

[Chestermiller]

Step 1: Find the velocity of the combined bullet and block immediately after impact of the bullet. This is the initial velocity for

Step 2: the problem of a bullet/block mass being slowed down by the compressing spring. Treat the bullet/block combo as a free body, and write the 2nd law force balance equation on it.