Tacoma Narrows Bridge disaster and Trigonometric functions?

Question

How does the collapse of the Tacoma Narrows bridge relate to trigonometric functions?
If you had been the architect/engineer of the Tacoma Narrows Bridge, what might you have done differently?

Answer 1

I wouldn't have built the bridge in such a way that the winds that blew across it wouldn't have caused my bridge to oscillate at a harmonic frequency thus destroying it due to the cataclysmic reaction caused by such.

Answer 2

It's a bit of a stretch, but I suspect that the reference is to the appearance of the bridge as the torsional waves reflected up and down its plate girder. Were you to plot the deflection angle of the bridge at one point with respect to time, you'd probably get something close to a sinuosoidal function, at least if the beam was behaving in a linear manner, which it may or may not have been.

For extra credit, you can point out that in a less-publicized incident at about the same time the Golden Gate bridge was nearly lost, in exactly the same way. Prompt retrofitting got underway in very short order. It took bridge builders a while to realize that you can't build suspension bridges with decks thin enough to make architects happy. Compare the thickness of the Tacoma Narrows (even its replacement) with that of the Brooklyn Bridge, designed with just such an eventuality in mind.

Answer 3

If the tacoma narrows bridge is the one that broke apart during a heavy wind storm, then it has more to do with Differential Equations than trig, but since trig is an intergral part of DE then here is the reason.

In diff. eq. you have a concept of "resonant frequency" this means, there is a frequency that any object vibrates at. if you are able to recreate this vibrational frequency and direct it at that object, you can cause the vibrations to increase in amplitude. To avoid this amplitude re-inforcement, engineers build dampening effects into this object to avoid a catastrophic result. In the case of the bridge, the resonant frequency of the wind blowing over top and below came close enough to the resonant freq of the bridge to cause it to basically disintegrate on a molecular level. If i were to have built the bridge, i would have created damping effects to prevent this from happening that easily.

Answer 4

Do my own homework,for starters.