It's not a separate spring. The thin steel disc that the lining is riveted to is stamped into a 'wavy' pattern when it is made. This gives it a springiness-if you look at the edge of a disc you can see a gap between the two linings. This gives a cushioning effect as the the clutch pedal is released, so engagement is gradual, as the 'springy' disc is compressed, instead of an all or nothing engagement.