I guess folks need different levels of instruction. I thought a close-up photo of the removal of the spring offered sufficient content. Anyway, the tech at the dealer said he had removed and lubed these springs in several M3 cars, and it was the problem in each case, including mine. He had not seen the problem in any other models. If this is the issue in your car, you can definitely hear the difference in this sound, compared to something being caught between rotor and shield. The sounds are similar (having heard both), but this definitely has a “springy” quality that is unmistakable. And, if the issue is something caught in there, the object can easily be dislodged by pressing the shield away from the rotor with a long screwdriver. If nothing falls out, then you have another problem, which may be these springs.
2011 Space Gray Coupe, DCT, ZCP, StopTech ST-60/ST-40 BBK.