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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After the positions were recorded for frequencies 1,803 Hz, 2,402 Hz, 3,002 Hz, 3,600 Hz, and 4,201 Hz, the wavelength was determined for each. This was done by subtracting the initial position from the final position (position final–position initial=wavelength). Using the calculated wavelength, the speed of sound in air at each frequency was determined by multiplying the wavelength by the frequency (speed of sound=wavelength x frequency). By adding the five speed values and dividing by the number of speeds, the average speed of sound was calculated. Then 344 m/s was used as the accepted

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at octave frequencies between 250 Hz and 4 kHz) was carried out and an average pure-tone

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My dependent variable how much weight each bridge can endure before the bridge breaks apart. When you add weight tension is created. (tension is a pulling force that occurs at the bottom of a bridge) when tension is applied the connecting points (glue, pieces that snap together, etc.) will unconnect so everything will fall apart and the bridge collapse to the ground.

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One of the most influential engineering discoveries in the past century was the ill-fated Tacoma Narrows Bridge. “Galloping Gertie” as she was known to local residents, the massive Washington state suspension bridge shook, rattled and rolled its way into the history books. Legendary in its time, the Tacoma Narrows Bridge held many records and drew tourists from around the world in its short life. However, the famous bridge is not known for its creative engineering or speedy construction, unfortunately the bridge was destined to fail. That failure in turn changed the way every building is constructed today as well as further man’s understanding of physics and the forces of nature. In this paper we

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Create a simple model using Matlab, simulating the multi-storey structure which returns all the natural frequencies from the numerical methods in the model.

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In this method, the challenges from that emanated from the previous methods are solved through the development of a quicker way that solves the same problems in a short duration. The goal of the project was to obtain an easier methodology that can help in solving systems of eigen problems. In particular the study aimed at obtaining anything that solve a collection of problems. The new methodology adopted not only maintains the solution requirements but also introduces systematic improvability. Through the new insights added to the new method which distinguishes it from the previous methodologies, the required accuracy coupled with a fewer degree of freedom can be achieved.

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Thus, components like a mast or bridge girder can be analysed more comprehensively with compartively with lesser degrees of freedom.

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