"These traps are probably 80% "hole" and 20% steel and have some springiness, so intuitively they should have some damping properties."
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You have it wrong. Springy and damping are not the same thing. These act as springs, as you noted, so they change the resonance characteristics of the system. They cannot provide any damping.
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You have it wrong. Springy and damping are not the same thing. These act as springs, as you noted, so they change the resonance characteristics of the system. They cannot provide any damping.