refer to here:
One of the most famous examples of a resonance disaster is the 1940 Tacoma Narrows Bridge collapse in Washington, USA. This came about not simply as a result of mechanical resonance, but also aeroelastic flutter – a process that occurs when complex, varying oscillations are caused by passing winds.
Leaving the issue of aeorelastic flutter aside, I understand that resonant frequency can somewhat increase the vibration of the bridge, and hence may result in the collapse of a bridge.
But I fail to see this, from the known physics laws. Any mathematical derivation for this from the first principles?