As long as you want hard body dynamics it should be pretty straight forward.  Model a pendulum, punch a hole in the top where you want the pivot point.  Run a cylinder through that.  Enable physics on the pendulum object and hit the calculate physics button.  That should be it.

As for applying physics to a group, I'm not sure.  What kind of group?  If you want the objects in the group to act independently I'm guessing you'll need to turn on physics for each item individually.

I've attached a .car file that I set up I had to rename the extension to .jpg so hopefully it will still work once you change that back to .car.

I hope this helps.