If the chain is taut like a guitar string, all you have to do is play it. The vibration will drive the castle dwellers crazy, and might even cause property and biological damage. Every chamber in the castle will potentially act as a small resonance chamber as well.

To play the chain, use it as target practice for trebuchets. Hit it once, and you've got it calibrated for the next strum. Use something softer than the chain's material as ammo in order to avoid damaging it (too much).

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If the rope is not taut, your engineers may find a way to yank it. Pull it taut and let go, and every castle dweller will become a reddish goo stuck to a wall.