How Can Eigenvalues Calculate Resonance Factors?

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Eigenvalues can be used to calculate resonance factors, which are important when constructing infrastructure, such as bridges and skyscrapers. If a wind or some force consistently hits the bridge or building at the precise resonance factor, then the distance the structure sways can increase significantly when considering the summation of all of the forces, leading to the structures demise. An example of this would be the Tacoma Bridge in 1940 when the engineers failed to account for resonance and therefore ignored the natural frequency of the bridge being magnified by an identical frequency, in this case the 42 mph wind. The natural frequency can be calculated using the magnitude of the smallest eigenvalue and by solving natural frequencies
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