The car's corner mass is m, and the unsprung mass is m₂. The suspension spring stiffness is k, the tire stiffness is k,, and c is the suspension damping coefficient. The car is traveling at speed Von a sinusoidal road surface with amplitude A, and wavelength . Draw free body diagrams for the corner mass and the unsprung mass, derive the system's equations of motion, and put them in vector-matrix form. Notice that up is the positive direction for all the coordinates in this problem. Answer: k 0 2[***¯ {^,.A, sin aut "} -k₂ k₂ + k₂ ot m₂ 0 0 m₂ C -C m₂ 2 k₂ k₁ m₂ www -k₂ 2₂ 2₁ z, (t) = A, sin ot where @= 2&V 2

The car's corner mass is m, and the unsprung mass is m₂. The suspension spring stiffness is k, the tire stiffness is k,, and c is the suspension damping coefficient. The car is traveling at speed Von a sinusoidal road surface with amplitude A, and wavelength . Draw free body diagrams for the corner mass and the unsprung mass, derive the system's equations of motion, and put them in vector-matrix form. Notice that up is the positive direction for all the coordinates in this problem. Answer: k 0 2[***¯ {^,.A, sin aut "} -k₂ k₂ + k₂ ot m₂ 0 0 m₂ C -C m₂ 2 k₂ k₁ m₂ www -k₂ 2₂ 2₁ z, (t) = A, sin ot where @= 2&V 2

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

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.

Question

The car's corner mass is m, and the unsprung mass is m₂. The suspension spring
stiffness is k, the tire stiffness is k, and c is the suspension damping coefficient. The
car is traveling at speed Von a sinusoidal road surface with amplitude A₁ and
wavelength 2. Draw free body diagrams for the corner mass and the unsprung mass,
derive the system's equations of motion, and put them in vector-matrix form. Notice
that up is the positive direction for all the coordinates in this problem.
Answer:
k₂ -k₂
0
0
Z₁
m₂
[KH[ K**}-{4.A, sin ort
+
0 m2₂
-k₂ k₂ + k₁₂
с
-C с
m₂
+
k₂
k₂
m₂
Z₂
=
N
22₂
12₁
z, (t) = A, sin @t
where @
2+V
2

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