Vibrations Question A building is modeled and subjected to ground motion such as a 4.5 magnitude earthquake as shown below. The building is modeled as a single–degree–of–freedom (SDOF) mass–spring system where the building mass is lumped atop of two beams used to model the walls of the building in bending. Assume the ground motion is modeled as having amplitude of 0.2 m at a frequency of 8.5 rad/s, the building mass is 150000 kg, and the stiffness of each wall is 4.519 x 10^6 N/m. r=1.095 wn=7.762rad/s mx''(t)+2kx(t)=0.2cos(8.5*t) Explain if the building will break after the earth quake.  Give steps to use MATLAB to obtain the vibratory response due to the earthquake when the building is in bending relative to ground for 0 ≤ t ≤ 25s. Assume zero initial conditions.

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Vibrations Question

A building is modeled and subjected to ground motion such as a 4.5 magnitude earthquake as shown below. The building is modeled as a single–degree–of–freedom (SDOF) mass–spring system where the building mass is lumped atop of two beams used to model the walls of the building in bending. Assume the ground motion is modeled as having amplitude of 0.2 m at a frequency of 8.5 rad/s, the building mass is 150000 kg, and the stiffness of each wall is 4.519 x 10^6 N/m.

r=1.095 wn=7.762rad/s

mx''(t)+2kx(t)=0.2cos(8.5*t)

Explain if the building will break after the earth quake.

 Give steps to use MATLAB to obtain the vibratory response due to the earthquake when the building is in bending relative to ground for 0 ≤ t ≤ 25s. Assume zero initial conditions.

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