# Homework Help: Oscillator with and without damping - Need help please

1. Oct 18, 2011

### 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(ωdt) [Under-damping eqn of motion] when x>0

Well 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.

2. Oct 18, 2011

### 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.

3. Oct 18, 2011

### Fjolvar

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

4. Oct 18, 2011

### Fjolvar

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

5. Oct 19, 2011

### Fjolvar

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