Is damping forces change period of any oscillation system?

I have very little knowledge in this area. I am not sure what you are looking for but I believe I know of two examples of damping.

One was in a documentary on TV about certain skyscrapers having a damping system on the top floor, which minimizes the amount of sway the building experiences.
The other is I know that damping is used on some large power transmission cables to prevent harmonics I believe. Hope this is of some help.