How was the displacement for the spring between each of the masses obtained in the first picture? They were highlighted in yellow. Please explain, the topic is really confusing. Also in the second picture how will this be written for each of the masses? You don't have to determine the state space representation of the second pic, just explain what the displacement for the spring will be for each masses. FIGURE 3.4Two rolling cartsattached withsprings anddampers.k₂q(t)b₂ġ(t)[b₂u(t)InputforceM₂M₂q(t)m1q(t)Cart 2x(t)Mb₁•k₁q (1)-k₁p (1)• b₁q(t)-b₁p(t)M₁k₁Voyk₁p(t)-k₁q(1)b₁p(t)-b₁ġ(t)(a)(b)FIGURE 3.5 Free-body diagrams of the two rolling carts. (a) Cart 2; (b) Cart 1.p(t)Cart 1E3.16 Two carts with negligible rolling friction are con-nected as shown in Figure E3.16. An input force is u(t).The output is the position of cart 2, that is, y(t) = q(t).Determine a state space representation of the system.m2u(t)M₁q(t)k₂Mp(t)b₂→u(t)

From the figure 3.5, The forces acting on the body of mass 'M2' are given by,k2q(t) in the opposite…

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Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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How was the displacement for the spring between each of the masses obtained in the first picture? They were highlighted in yellow. Please explain, the topic is really confusing. Also in the second picture how will this be written for each of the masses? You don't have to determine the state space representation of the second pic, just explain what the displacement for the spring will be for each masses.

FIGURE 3.4
Two rolling carts
attached with
springs and
dampers.
k₂q(t)
b₂ġ(t)
[
b₂
u(t)
Input
force
M₂
M₂
q(t)
m1
q(t)
Cart 2
x(t)
M
b₁
•k₁q (1)-k₁p (1)
• b₁q(t)-b₁p(t)
M₁
k₁
Voy
k₁p(t)-k₁q(1)
b₁p(t)-b₁ġ(t)
(a)
(b)
FIGURE 3.5 Free-body diagrams of the two rolling carts. (a) Cart 2; (b) Cart 1.
p(t)
Cart 1
E3.16 Two carts with negligible rolling friction are con-
nected as shown in Figure E3.16. An input force is u(t).
The output is the position of cart 2, that is, y(t) = q(t).
Determine a state space representation of the system.
m2
u(t)
M₁
q(t)
k₂
M
p(t)
b₂
→u(t)

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