The relative displacement u(t) of a single-storey shear building subjected to an earthquakeground motion is represented by the following second-order linear ordinary differentialequation:d?udt2du+ c+ ku =a, (t)mdtwhere m, c, and k are the mass (kg), damping constant (Ns/m), and stiffness of thestructure (N/m), respectively. Meanwhile, a,(t) is the function of earthquake groundacceleration.Suppose the building with a mass of 2000 kg and supported by columns of combinedstiffness of 32 x 103 N/m is subjected to earthquake with ground acceleration given by thefollowing function:ag(t)= 36000 cos 2tFind the equation of the displacement, u(t), given the damping is not installed to thebuilding. Then, find how much the building is displaced from t =30 seconds to t =60 secondsof earthquake.

Write the differential equation. md2udt2+cdudt+ku=36000cos2tif damping is not installed…

The relative displacement u(t) of a single-storey shear building subjected to an earthquake ground motion is represented by the following second-order linear ordinary differential equation: d2u du + c + ku : a,(t) m %3D dt2 dt where m, c, and k are the mass (kg), damping constant (Ns/m), and stiffness of the structure (N/m), respectively. Meanwhile, a,(t) is the function of earthquake ground acceleration.

The relative displacement u(t) of a single-storey shear building subjected to an earthquake ground motion is represented by the following second-order linear ordinary differential equation: d2u du + c + ku : a,(t) m %3D dt2 dt where m, c, and k are the mass (kg), damping constant (Ns/m), and stiffness of the structure (N/m), respectively. Meanwhile, a,(t) is the function of earthquake ground acceleration.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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