Damped harmonic oscillator with a CONSTANT frictional force

[khfrekek92]

Homework Statement

There is a block attached to the wall via a spring. The only damping force is friction, where there is kinetic and static.

Homework Equations

m(d^2x/dt^2)=-kx-?

The Attempt at a Solution

I can solve this, except usually the damping force is given as (alpha)(velocity) where it is proportional to the velocity, however, this has a (mu)k and a (mu)s. What do I add on to my force equation??

Thanks in advance!

 

[khfrekek92]

So far I have m(d^2x/dt^2)=-k(x-Lo)-[mu]kmg
(d^2x/dt^2)=(d^2z/dt^2)=-kz/m-g[mu]k=-(sqrt(k/m))2z-g[mu]k

Then I find the solution to be z=Acos(sqrt(k/m)t+[phi])-.5[mu]k*gz^2

Am I on the right track?

Thanks!