Determine the equation of motion in a matrix form using Newton's second law, [m]y+ [c]y + [k]y = F. By omitting the damping and external force parameter, deduce and express the general solution in the form of ([k] – w*[m]){Y} = 0. Analyze the maximum vertical displacement at each floor when the system's natural frequency is equal to the external stimulation frequency. Assume nontrivial solution and F1,2,3(t) exhibits harmonic oscillation of sin 0.02t. Describe an eigenvector using a three-degree-of-freedom system's mode form as an illustration for wl, w2> wl and w3 > w2 > wl.

Determine the equation of motion in a matrix form using Newton's second law, [m]y+ [c]y + [k]y = F. By omitting the damping and external force parameter, deduce and express the general solution in the form of ([k] – w*[m]){Y} = 0. Analyze the maximum vertical displacement at each floor when the system's natural frequency is equal to the external stimulation frequency. Assume nontrivial solution and F1,2,3(t) exhibits harmonic oscillation of sin 0.02t. Describe an eigenvector using a three-degree-of-freedom system's mode form as an illustration for wl, w2> wl and w3 > w2 > wl.

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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Concept explainers

Forced undamped vibrations

In mechanical engineering, vibration is expressed as the term that occurs due to an object's backward and forward movement about a point of equilibrium. Generally, there are three types of vibrations which are,

Question

b) Determine the equation of motion in a matrix form using Newton's second law, [m]y+
[c]y + [k]y = F.
c) By omitting the damping and external force parameter, deduce and express the general
solution in the form of ([k] – w[m]){Y} = 0.
d) Analyze the maximum vertical displacement at each floor when the system's natural
frequency is equal to the external stimulation frequency. Assume nontrivial solution
and F12,3(t) exhibits harmonic oscillation of sin 0.02t.
e) Describe an eigenvector using a three-degree-of-freedom system's mode form as an
illustration for wl, w2 > w1 and w3 > w2 > wl.

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