Almost immediately - it collapsed the same year it opened.The Tacoma bridge appeared to be an engineering marvel until the wind got it to its resonant frequency.
It's actually a perfect example of hubris and taking assumptions too far, the designer had expressed his admiration for the slender bridge decks of early British suspension bridges like the Menai Straights, seemingly not realising that most of them had been replaced on numerous occasions due to wind damage. The bridge was well beyond the envelope of what was understood or had been experienced at the time.
It's also, strictly speaking, not related to resonant frequency, but explanations of what was actually going on tend to get bogged down in terms like "aeroelastic flutter" that are rather harder to explain in a GCSE Physics class.