4 Problem 4: A car body with mass m and pitching inertia I is attached to the front and rear axles,mr and mr, by suspension spring ks and dampers bs. Each tire has a stiffness kt. The inputs are theroad height profiles rf (t) and r,. (t) experienced by the front and rear tires.a) Clearly identify all the degrees of freedom andlabel them clearly on the diagram below. Thecenter of mass is marked with a .b) Draw and clearly label all relevant free-body diagrams for the system.L2L1Car body me, IksbsMrr.(t)ktksbsktmTf(t)mimc) Write an equation of motion (Newton's 2nd law) for the rotational degree of freedom of thecar body only.d) How many state variables are required to describe the system?e) How many modes does the system have?f) Are any of the eigenvalues of the system matrix purely imaginary (i.e. s=iwn)? Yes No.Briefly explain your reasoning:g) Do any of the eigenvalues of the system matrix have positive real parts? Yes No.Briefly explain your reasoning:

Answered: Image /qna-images/answer/502f1ff5-d88f-4ce2-83d1-3d4c787b3f6b.jpg

Problem 4: A car body with mass m and pitching inertia I, is attached to the front and rear axles, mr and mr, by suspension spring k, and dampers bs. Each tire has a stiffness kt. The inputs are the road height profiles rf (t) and r,(t) experienced by the front and rear tires. a) Clearly identify all the degrees of freedom and label them clearly on the diagram below. The center of mass is marked with a O. b) Draw and clearly label all relevant free- body diagrams for the system. ks Car body me, I bs ks bs mr mg r.(t) kt kt 'f(t) www c) Write an equation of motion (Newton's 2nd law) for the rotational degree of freedom of the car body only.

Problem 4: A car body with mass m and pitching inertia I, is attached to the front and rear axles, mr and mr, by suspension spring k, and dampers bs. Each tire has a stiffness kt. The inputs are the road height profiles rf (t) and r,(t) experienced by the front and rear tires. a) Clearly identify all the degrees of freedom and label them clearly on the diagram below. The center of mass is marked with a O. b) Draw and clearly label all relevant free- body diagrams for the system. ks Car body me, I bs ks bs mr mg r.(t) kt kt 'f(t) www c) Write an equation of motion (Newton's 2nd law) for the rotational degree of freedom of the car body only.

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

Problem 4: A car body with mass m and pitching inertia I is attached to the front and rear axles,
mr and mr, by suspension spring ks and dampers bs. Each tire has a stiffness kt. The inputs are the
road height profiles rf (t) and r,. (t) experienced by the front and rear tires.
a) Clearly identify all the degrees of freedom and
label them clearly on the diagram below. The
center of mass is marked with a .
b) Draw and clearly label all relevant free-
body diagrams for the system.
L2
L1
Car body me, I
ksbs
Mr
r.(t)
kt
ksbs
kt
m
Tf(t)
mim
c) Write an equation of motion (Newton's 2nd law) for the rotational degree of freedom of the
car body only.
d) How many state variables are required to describe the system?
e) How many modes does the system have?
f) Are any of the eigenvalues of the system matrix purely imaginary (i.e. s=iwn)? Yes No.
Briefly explain your reasoning:
g) Do any of the eigenvalues of the system matrix have positive real parts? Yes No.
Briefly explain your reasoning:

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