Oscillator with and without damping - Need help please

[Fjolvar]

An oscillator with natural frequency ω consists of a mass on a spring positioned on a horizontal table. The table is frictionless for x<0 but has friction for x>0 and an effective damping constant K on that side of the table. Find the frequency of this oscillator and the ratio of successive amplitudes. Assume K<ω (Under-damping).
Relevant equations
x=C*cos(ωt) [Eqn of motion w/o damping] when x<0
x=Ce^-Kt cos(ω_dt) [Under-damping eqn of motion] when x>0Well it seems there will be two parts of the problem for each side of the table, which means it will probably be one quantity plus another. Any help getting started on this problem would be greatly appreciated. Thank you in advance.

 

[Eynstone]

It won't be simply the sum of the two. It will consist of alternate pieces of the graphs of the two. We must consider the time intervals in which x>0 & x<0 separately.

 

[Fjolvar]

Any others? I don't really think I need to use the graph on this one.

 

[Fjolvar]

I've been stuck on this problem for a few days. I just can't see how to reduce it to one equation..

 

[Fjolvar]

Any ideas? Class will be starting relatively soon and I've still yet to figure this one out. Any help much appreciated.. thanks.