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dynamic analysis - Tacoma Narrows - pushover analysis?

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Interesting conversation about Tacoma narrows:

Reasons a dynamic analysis is necessary -  i.e. self-excitation !
This is pretty much the same as the frequency of the structure at
the frequency of the load, but with additional factors that actually 
increase the structure's response for each cycle.

Hey this is like those kinetic watches that you just shake your wrist,
andthe watch keeps on ticking ...

Further question about qualifying a dynamic analysis...

Cannot a pushover analysis take the place of a dynamic analysis.
Sometimes this is the more complicated method, and takes into
account the ductility of the structure much more readily than a 
time-history or spectrum analysis, no?  This is probably more suitable
for performance based design?

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