Is there a way to make parts wave around naturally?

Hi, this is my first time animating and I couldn’t find information on how to make certain body parts wave around when others move. For example, if a cat is walking, its tail will follow, waving around according to the motion of pelvis. Is there a quick way to simulate this in Blender?

I’m currently training animation with this little 3 hour quickie

The file can be found in the end of this thread for anyone interested in checking out, or explaining me what’s going on. Also, there are probable faults in the bones, so please feel free to give me any critique relating the whole project.

The file: