Answered: The figure that is attached illustrates…

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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Question

The figure that is attached illustrates a system in which a force F is applied to a mass m2 that is connected to another mass m1 via a spring and a damper, and mass m1 is connected to a wall via a damper. The equations of motion that govern the time evolution of the mass displacements, y1(t)and y2(t), are given below.

A) Define 4 state variables of the system (xi, i = 1,…,4) as phase variables, and define the control input u. Convert the two equations of motion above into four 1st
-order ODEs that are functions of the state variables and the control input.
(b) Write the four 1st -order ODEs from part (a) in state-space form,
x = Ax+Bu.

nt illustrates
a system
applied to a mass m2
nother mass mi via a
er, and mass mi is
via a damper. The
that govern the time
s displacements, yı(t)
-elow.
b₁
Đ m₁
Y₁
b₂
D
www
k
m₁ÿ₁ = k(y₁ - y₁) − b₁ỳ₁ + b₂(₂-₁)
m₂Ÿ₂ = k(y₁ - y₂) + b₂(y₁ - y₂) + F
m2
Y₂
F

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