Answered: b) Determine the equation of motion in…

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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A three-level offshore platform located in the Helang Oilfield area has a 1500 kg floor
steel grating supported at each level. The structure sometimes is subjected to a vertical
oscillation movement during rough sea waves given by function of ?(?) = ? sin ??.
If the steel grating only moves in the vertical direction and is supported by one
equivalent spring and damper at each steel grating pole level with stiffness, k1 = (600) N/m, k2 = (400) N/m and k3 = (200) N/m while damping, c1 = (105)
Ns/m, c2 = (70) Ns/m and c3 = (35) Ns/m, respectively, as simplified in Figure
Q1. Neglect the effect of gravitational force.

(Please answer the all question I was upload for so many times but I didn't get proper answer Pls!)

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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