Song, (first tone in Mandarin) often written sung, is a homonym with pine tree, it means to let go of status, to slack, to relax and to sink.
Zhong means "center," as in Zhongguo (China, center country).
Jin means a type of power which can be cultivated through practice. The word is almost always used in compound form and so it can mean widely different things, like gongjin (empty force, pushing without touching), or tingjin (sensitivity, literally "hearing power").
I believe that song zhong jin means something like: Non-structural power. Perhaps it means power which does not rely on a clear center. It may even mean power which is not transfered or generated through the back, the spine, the bones, or the centerline.
What do you all say?