What caused the millennium bridge in London to wobble?

Structural resonance.

When the bridge first opened in 2000, pedestrians walking in step with each other caused vertical oscillations with an amplitude up to 1 in (25 mm). Although this did not pose any danger of structural damage or collapse this effect was disconcerting to pedestrians; the lateral swaying, though smaller in amplitude (about 0.25 in or 6 mm), was far more visible. The bridge was closed, and fitted with dampers to increase its dynamic rigidity by over tenfold without sacrificing much comfort by its engineers Ove Arup.

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