In this system, there are two mass elements: m, and m₂. They are con- nected by a spring. m₁ is also connected to a massless rod, which can rotate at its midpoint. The other end of this massless rod is connected to another massless rod, which is connected to the ground through a spring and a damper. This configuration forms the basis of the system. You may assume small deflections for this problem and that the vertical connections are rigid links. When the coordinates y₁, 92, y are equal to zero, the gravi- tational force on the masses is covered by springs (the system is at its static deflection). Two input forces, fi and f2, are applied on the masses m₁ and m2 respectively. HINT: You should not consider the gravity force in your solution. Your tasks: A Short Answer: Which elements (refer to them by their corresponding constants) can store or possess energy in this system? B Draw the FBD for each mass (one for each of m₁ and m2. C Derive the equations of motion for the masses with y₁ and y2 as the dynamic variables. Please put the dynamic variables on the left- hand side and the input terms on the right-hand side. = D BONUS: If the system is at an instantaneous condition where yı 1 [m/s], 1 = Ÿ2 2 = 1 [m/s2], f₁ = 1 [N], f2 = 3 [N], m₁ = 1 [N/m], c= 1 [Ns/m]. m₂ = 1 [kg], k₁= k2 deflection in spring k₁? What is the =
In this system, there are two mass elements: m, and m₂. They are con- nected by a spring. m₁ is also connected to a massless rod, which can rotate at its midpoint. The other end of this massless rod is connected to another massless rod, which is connected to the ground through a spring and a damper. This configuration forms the basis of the system. You may assume small deflections for this problem and that the vertical connections are rigid links. When the coordinates y₁, 92, y are equal to zero, the gravi- tational force on the masses is covered by springs (the system is at its static deflection). Two input forces, fi and f2, are applied on the masses m₁ and m2 respectively. HINT: You should not consider the gravity force in your solution. Your tasks: A Short Answer: Which elements (refer to them by their corresponding constants) can store or possess energy in this system? B Draw the FBD for each mass (one for each of m₁ and m2. C Derive the equations of motion for the masses with y₁ and y2 as the dynamic variables. Please put the dynamic variables on the left- hand side and the input terms on the right-hand side. = D BONUS: If the system is at an instantaneous condition where yı 1 [m/s], 1 = Ÿ2 2 = 1 [m/s2], f₁ = 1 [N], f2 = 3 [N], m₁ = 1 [N/m], c= 1 [Ns/m]. m₂ = 1 [kg], k₁= k2 deflection in spring k₁? What is the =
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
Related questions
Question
![In this system, there are two mass elements: m₁ and m₂. They are con-
nected by a spring. m₁ is also connected to a massless rod, which can
rotate at its midpoint. The other end of this massless rod is connected to
another massless rod, which is connected to the ground through a spring
and a damper. This configuration forms the basis of the system. You may
assume small deflections for this problem and that the vertical connections
are rigid links. When the coordinates y₁, y2, y are equal to zero, the gravi-
tational force on the masses is covered by springs (the system is at its static
deflection). Two input forces, fi and f2, are applied on the masses m₁ and
m2 respectively.
HINT: You should not consider the gravity force in your solution.
Your tasks:
A Short Answer: Which elements (refer to them by their corresponding
constants) can store or possess energy in this system?
B Draw the FBD for each mass (one for each of m₁ and m₂.
H
C Derive the equations of motion for the masses with y₁ and y2 as the y₂
dynamic variables. Please put the dynamic variables on the left-
hand side and the input terms on the right-hand side.
D BONUS: If the system is at an instantaneous condition where yı
1 [m/s], ₁ = 2 = 1 [m/s²], f₁ = 1 [N],
1 [N], f2 = 3 [N], m₁ =
What is the
1 [kg], k₁= k₂= 1 [N/m], c = 1 [Ns/m].
deflection in spring k₁?
m2
kı
=
У1'
=
fil
m₁
M₂
f2
a
K₂
a
H
ww
k₁
JC
Figure 1: System schematic.
y](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4c49c29d-b734-4891-8a07-7c122a77a78d%2Fc8fc620f-8bfb-43c8-90d4-3d0b0bbd081b%2Fs7p8x1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In this system, there are two mass elements: m₁ and m₂. They are con-
nected by a spring. m₁ is also connected to a massless rod, which can
rotate at its midpoint. The other end of this massless rod is connected to
another massless rod, which is connected to the ground through a spring
and a damper. This configuration forms the basis of the system. You may
assume small deflections for this problem and that the vertical connections
are rigid links. When the coordinates y₁, y2, y are equal to zero, the gravi-
tational force on the masses is covered by springs (the system is at its static
deflection). Two input forces, fi and f2, are applied on the masses m₁ and
m2 respectively.
HINT: You should not consider the gravity force in your solution.
Your tasks:
A Short Answer: Which elements (refer to them by their corresponding
constants) can store or possess energy in this system?
B Draw the FBD for each mass (one for each of m₁ and m₂.
H
C Derive the equations of motion for the masses with y₁ and y2 as the y₂
dynamic variables. Please put the dynamic variables on the left-
hand side and the input terms on the right-hand side.
D BONUS: If the system is at an instantaneous condition where yı
1 [m/s], ₁ = 2 = 1 [m/s²], f₁ = 1 [N],
1 [N], f2 = 3 [N], m₁ =
What is the
1 [kg], k₁= k₂= 1 [N/m], c = 1 [Ns/m].
deflection in spring k₁?
m2
kı
=
У1'
=
fil
m₁
M₂
f2
a
K₂
a
H
ww
k₁
JC
Figure 1: System schematic.
y
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