The question of predictability of the nature of the lateral motions of the Millennium Bridge will doubtless provide a subject for a full debate in due course.
The phenomenon of 'locking-in' of the frequency of the disturbing force, when this approximates to the natural frequency of the structure, occurs elsewhere.
For example, this is also a feature of the vortex stream for a cylinder in a steady current of air or water.
Another similarity is that here also the transverse oscillation caused by the vortex-shedding, which corresponds to the lateral motion of the bridge, will have a natural frequency half that of the rarer in-line oscillation, observed by Sainsbury and King at the Immingham Jetty (Proceedings of the ICE 49, 269-302), which corresponds to the vertical motion of the bridge.
Sir Alan Muir Wood (F), Franklands, Bere Court Road, Pangbourne, Berks, RG88JY