Question: ![enter image description here](https://i.stack.imgur.com/GHBz0.jpg)

So I'm a hobbiest who loves doing and learning about different subjects. Often I run into difficult problems that I normally can find solutions to however this one stumped me, I have reviewed many physics journals on the problem but either they are two complex or tackle the much easier version of 'viscous' friction.(p 2/54)
Essentially when I even begin a solution I yield to this:

Ma = sign(v) \* mg\*mu - kx

This would be simple if the friction didn't change direction. Does anyone have a suggestion on how to approach this problem? I'm not looking for someone to solve it I just want an idea on how to start it. Thank you

Answer: 
For this type of use and to make it simple we will calculate the Pitting resistance equivalent number. This is based upon the material composition.

PREN = 1 x %Cr + 3.3 ( %Mo + 0.5 x %W ) + 16 x %N

First of all, I would not test any steel that have a PREN inferior to 40.

Here we are left with Super Duplex, Hyper Duplex and Super Austenitic. 

Then I would only choose steels made with very high end manufacturing processes in order to avoid any pollution. The heat treatment is also very important. Electropolishing can help to clean the surface.

Classical Super Austenitic include 904L, 254 SMO, AL-6XN, F44...

I prefer Duplex over Austenitic because it has better mechanical properties as long as you don't encounter very high temperatures. 

Classical Super Duplex include F53, F55... These could be very interesting to test.

Super Duplex does not corrode easily. It usually happens at high temperatures or pressures. But let's say that there are very very bad conditions in this mechanism... We would be left with Hyper Duplex like 2707 or 3207. The good point of these steels is that these have the best mechanical characteristics available for this type of use.
You could chrome plate the steel and it would work fine. Steel rims that are plated with chrome last for a very long time on cars on roads that are heavily covered in salt during the winter.