Brake drum

Can someone tell me what the spring is for that goes around the outside of the drum? I only have it on one drum

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The spring is to reduce drum harmonics. If you've ever rubbed a wet finger around the rim of a crystal wine glass, you'll know what I mean. When you turn a drum on a brake lathe, you need to add a dampening belt for the same reason. Once the harmonics start, they get worse if they're not dampened, and they result in vibration and reduced braking performance (not to mention the noise). Steel drums seemed to have more of a problem with that than the cast iron drums. Most aftermarket drums don't have the groove for the spring and don't seem to have the problem, so, don't transfer the spring over to them as they may not stay where they should.