Simple Damped Harmonic Oscillator with friction

a block of mass m=.5kg is sliding on a horizontal table with coefficients of static and kinetic friction of .8 and .5 respectively. It is attached to a wall with a spring of unstretched length l=.13m and force constant 200 n/m. The block is released from rest at t=0 when it is x=.23m from the wall. Where will it end up at long times?

I've drawn my diagram and set z=x-l, so z'=x' and z''=x''.
next, using f=ma, I got that:
mx''=-k(x-l)-[mu]k*mg
z''=-kz/m-[mu]kg
z''=-(sqrt(k/m))^2*z-[mu]k*g

Then I found the homogeneous and particular solutions to get:
z=Acos(sqrt(k/m)t+[phi])-.5[mu]k*gz^2
x=Acos(sqrt(k/m)t+[phi])-.5[mu]k*g(x-l… +l

Now I am lost.. Where do I go from here? Is this solution even right so far?
For hints our teacher gave us that "at long times" means to just pay attention to the particular solution.. And that using the static friction, we need to check the block at EACH turn-around to see if it has enough energy to turn around using:
k(x-l)>=[mu]s*mg, so
x>=[mu]s*mg/k + l

How do I check this? I don't know what phi or A is so how can I check x at each turn around?

All I know is that at t=0, x=.23 and x'=0

Thanks so much in advance! I really really appreciate it!!

200 x = 0.8*0.5*9.8 or x = 0.0196 m = 1.96 cm
It can stop at 0.23 + 0.0196 = 0.2496 or 0.2104 m