Begin by drawing in the darkest shadows that you see, but don't darken them all the way yet. Like drawing fabric shadow shapes, I draw "reflection shapes" of the shapes I see that are created by the reflections on the metal object. So on the pivot arm I've added shadows, and on the arm itself I've drawn reflection shapes. When shading reflective objects, the shadows often have sharp edges, so you might want to have your pencil pretty sharp as well.