OK this is what I have,

Natural frequency = 2/0.57 = 3.51Hz

Spring stiffness 3.51Hz = 1/2pi x square root of K/m (k works out to be about 2915)

Critical damping square root of 4mk = 264.5

I need the damping ratio to find actual damping and actual frequency, I don't think I can do it without a velocity?

The 5% of amplitude must come into it somehow?