Anharmonic oscillator without friction 
My friend and I are doing a project on physics at the university. We want to describe the non-harmonic oscillator, so we built the system shown in the picture.
The problem is there is friction between the cable and the weight that is hard to calculate. We want the friction to be as little as possible so we can neglect it in our analysis. We use some oil but we aren't sure that this is enough. We also want to change the cable to a thinner one but still, there could be a problem with friction.
Any advice to decrease the friction?
 A: The point of such experiments is less to get them right and more to learn from them. So try it out!
Gather your data, as carefully as you can, and analyze it supposing friction is negligible. You'll either obtain good fits - in which case you're done - or bad ones - in which case you can explain that perhaps friction is the culprit.
Better still: if friction seems relevant and you can't tackle the system with friction analytically, as you comment, solve it numerically and, by tweaking the friction constant, check whether that can give you a good fit. Maybe it still won't, there might be something else going on and then you can try again to figure out what that is. The more problems you face and try to solve, the more difficult and time consuming it'll be, but also the more you'll learn.
If the possibility of bad grades for a "failed experiment" worries you, it shouldn't: a good teacher will not judge you by the problems you face, but by how you deal with them.
As for whether you should expect the friction to be negligible or not, we don't have access to your setup - but you do. Measure it. If we assume the rate of energy loss to be a constant fraction of the energy, we expect an exponential decay with time for the oscillator amplitude. If the measurements confirm that, you'll at the very least obtain an estimate for the time scale where friction should be negligible.
Good luck.
