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A machine of mass 100 kg is subjected to an external harmonic force with a frequency of 40 rad/s. The designer decides to mount the machine on an isolator to reduce the force transmitted to the foundation. The isolator can be considered as a combination of stiffness ( K) and damper (damping factor, ξ ) in parallel. The designer has the following four isolators:
1. K = 640 kN/m, ξ = 0.70
2. K = 640 kN/m, ξ = 0.07
3. K = 22.5 kN/m, ξ = 0.70
4. K = 22.5 kN/m, ξ = 0.07
Arrange the isolators in the ascending order of the force transmitted to the foundation.
1. K = 640 kN/m, ξ = 0.70
2. K = 640 kN/m, ξ = 0.07
3. K = 22.5 kN/m, ξ = 0.70
4. K = 22.5 kN/m, ξ = 0.07
Arrange the isolators in the ascending order of the force transmitted to the foundation.
- a)4−3−1−2
- b)3 −1− 2 − 4
- c)1 −3− 4 − 2
- d)1−3−2−4
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A machine of mass 100 kg is subjected to an external harmonic force wi...
C). The designer wants to reduce the force transmitted to the foundation by at least 80%.
To achieve this, the designer needs to determine the values of stiffness (K) and damping factor (C) for the isolator.
The force transmitted to the foundation can be calculated using the equation:
F_transmitted = (K / m) * x + (C / m) * v
Where:
F_transmitted is the force transmitted to the foundation
K is the stiffness of the isolator
m is the mass of the machine
x is the displacement of the machine
C is the damping factor of the isolator
v is the velocity of the machine
Since the designer wants to reduce the force transmitted to the foundation by at least 80%, we can set up the following equation:
F_transmitted / F_external = 0.2
Where:
F_external is the external harmonic force applied to the machine
Substituting the equation for F_transmitted, we have:
((K / m) * x + (C / m) * v) / F_external = 0.2
Since the external harmonic force is given as:
F_external = m * a
Where:
a is the acceleration of the machine
Substituting this into the equation, we have:
((K / m) * x + (C / m) * v) / (m * a) = 0.2
Simplifying the equation, we get:
(K * x + C * v) / (m * a) = 0.2
Since we know that the external harmonic force has a frequency of 40 rad/s, we can also relate the acceleration (a) to the displacement (x) and velocity (v) using the equation:
a = -w^2 * x
Where:
w is the angular frequency, given by w = 40 rad/s
Substituting this into the equation, we have:
(K * x + C * v) / (m * (-w^2 * x)) = 0.2
Simplifying further, we get:
(K + C * v / (-w^2)) = 0.2 * m
Since we want to find the values of K and C, we need another equation. The designer can choose to minimize the displacement (x) or the velocity (v). Let's assume the designer wants to minimize the displacement.
Therefore, we can set the equation for the displacement (x) equal to zero:
K + C * v / (-w^2) = 0
Simplifying this equation, we get:
K = C * v / (w^2)
Substituting this equation into the previous equation, we have:
(C * v / (w^2) + C * v) / (-w^2) = 0.2 * m
Simplifying further, we get:
C * v * (1 / (w^2) - 1) = -0.2 * m * w^2
Dividing both sides by v and simplifying, we have:
C * (1 / (w^2) - 1) = -0.2 * m * w^2 / v
Finally, we can solve for C:
C = (-0.2 * m * w^2 / v) / (1 / (w^2) - 1)
To achieve this, the designer needs to determine the values of stiffness (K) and damping factor (C) for the isolator.
The force transmitted to the foundation can be calculated using the equation:
F_transmitted = (K / m) * x + (C / m) * v
Where:
F_transmitted is the force transmitted to the foundation
K is the stiffness of the isolator
m is the mass of the machine
x is the displacement of the machine
C is the damping factor of the isolator
v is the velocity of the machine
Since the designer wants to reduce the force transmitted to the foundation by at least 80%, we can set up the following equation:
F_transmitted / F_external = 0.2
Where:
F_external is the external harmonic force applied to the machine
Substituting the equation for F_transmitted, we have:
((K / m) * x + (C / m) * v) / F_external = 0.2
Since the external harmonic force is given as:
F_external = m * a
Where:
a is the acceleration of the machine
Substituting this into the equation, we have:
((K / m) * x + (C / m) * v) / (m * a) = 0.2
Simplifying the equation, we get:
(K * x + C * v) / (m * a) = 0.2
Since we know that the external harmonic force has a frequency of 40 rad/s, we can also relate the acceleration (a) to the displacement (x) and velocity (v) using the equation:
a = -w^2 * x
Where:
w is the angular frequency, given by w = 40 rad/s
Substituting this into the equation, we have:
(K * x + C * v) / (m * (-w^2 * x)) = 0.2
Simplifying further, we get:
(K + C * v / (-w^2)) = 0.2 * m
Since we want to find the values of K and C, we need another equation. The designer can choose to minimize the displacement (x) or the velocity (v). Let's assume the designer wants to minimize the displacement.
Therefore, we can set the equation for the displacement (x) equal to zero:
K + C * v / (-w^2) = 0
Simplifying this equation, we get:
K = C * v / (w^2)
Substituting this equation into the previous equation, we have:
(C * v / (w^2) + C * v) / (-w^2) = 0.2 * m
Simplifying further, we get:
C * v * (1 / (w^2) - 1) = -0.2 * m * w^2
Dividing both sides by v and simplifying, we have:
C * (1 / (w^2) - 1) = -0.2 * m * w^2 / v
Finally, we can solve for C:
C = (-0.2 * m * w^2 / v) / (1 / (w^2) - 1)
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Community Answer
A machine of mass 100 kg is subjected to an external harmonic force wi...
For k = 640000 N/m
For k = 22500 N/m
Since ∈∝ Ft . So, if Ft ↓ that means∈↓ .
From figure :
∈4 < ∈3 < ∈1 < ∈2
4 < 3 < 1 < 2
Hence, the correct option is (A).
For k = 22500 N/m
Since ∈∝ Ft . So, if Ft ↓ that means∈↓ .
From figure :
∈4 < ∈3 < ∈1 < ∈2
4 < 3 < 1 < 2
Hence, the correct option is (A).
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A machine of mass 100 kg is subjected to an external harmonic force with a frequency of 40 rad/s. The designer decides to mount the machine on an isolator to reduce the force transmitted to the foundation. The isolator can be considered as a combination of stiffness ( K) and damper (damping factor, ξ ) in parallel. The designer has the following four isolators:1. K = 640 kN/m, ξ = 0.702. K = 640 kN/m, ξ = 0.073. K = 22.5 kN/m, ξ = 0.704. K = 22.5 kN/m, ξ = 0.07Arrange the isolators in the ascending order of the force transmitted to the foundation.a)4−3−1−2b)3 −1− 2 − 4c)1 −3− 4 − 2d)1−3−2−4Correct answer is option 'A'. Can you explain this answer?
Question Description
A machine of mass 100 kg is subjected to an external harmonic force with a frequency of 40 rad/s. The designer decides to mount the machine on an isolator to reduce the force transmitted to the foundation. The isolator can be considered as a combination of stiffness ( K) and damper (damping factor, ξ ) in parallel. The designer has the following four isolators:1. K = 640 kN/m, ξ = 0.702. K = 640 kN/m, ξ = 0.073. K = 22.5 kN/m, ξ = 0.704. K = 22.5 kN/m, ξ = 0.07Arrange the isolators in the ascending order of the force transmitted to the foundation.a)4−3−1−2b)3 −1− 2 − 4c)1 −3− 4 − 2d)1−3−2−4Correct answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A machine of mass 100 kg is subjected to an external harmonic force with a frequency of 40 rad/s. The designer decides to mount the machine on an isolator to reduce the force transmitted to the foundation. The isolator can be considered as a combination of stiffness ( K) and damper (damping factor, ξ ) in parallel. The designer has the following four isolators:1. K = 640 kN/m, ξ = 0.702. K = 640 kN/m, ξ = 0.073. K = 22.5 kN/m, ξ = 0.704. K = 22.5 kN/m, ξ = 0.07Arrange the isolators in the ascending order of the force transmitted to the foundation.a)4−3−1−2b)3 −1− 2 − 4c)1 −3− 4 − 2d)1−3−2−4Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A machine of mass 100 kg is subjected to an external harmonic force with a frequency of 40 rad/s. The designer decides to mount the machine on an isolator to reduce the force transmitted to the foundation. The isolator can be considered as a combination of stiffness ( K) and damper (damping factor, ξ ) in parallel. The designer has the following four isolators:1. K = 640 kN/m, ξ = 0.702. K = 640 kN/m, ξ = 0.073. K = 22.5 kN/m, ξ = 0.704. K = 22.5 kN/m, ξ = 0.07Arrange the isolators in the ascending order of the force transmitted to the foundation.a)4−3−1−2b)3 −1− 2 − 4c)1 −3− 4 − 2d)1−3−2−4Correct answer is option 'A'. Can you explain this answer?.
A machine of mass 100 kg is subjected to an external harmonic force with a frequency of 40 rad/s. The designer decides to mount the machine on an isolator to reduce the force transmitted to the foundation. The isolator can be considered as a combination of stiffness ( K) and damper (damping factor, ξ ) in parallel. The designer has the following four isolators:1. K = 640 kN/m, ξ = 0.702. K = 640 kN/m, ξ = 0.073. K = 22.5 kN/m, ξ = 0.704. K = 22.5 kN/m, ξ = 0.07Arrange the isolators in the ascending order of the force transmitted to the foundation.a)4−3−1−2b)3 −1− 2 − 4c)1 −3− 4 − 2d)1−3−2−4Correct answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A machine of mass 100 kg is subjected to an external harmonic force with a frequency of 40 rad/s. The designer decides to mount the machine on an isolator to reduce the force transmitted to the foundation. The isolator can be considered as a combination of stiffness ( K) and damper (damping factor, ξ ) in parallel. The designer has the following four isolators:1. K = 640 kN/m, ξ = 0.702. K = 640 kN/m, ξ = 0.073. K = 22.5 kN/m, ξ = 0.704. K = 22.5 kN/m, ξ = 0.07Arrange the isolators in the ascending order of the force transmitted to the foundation.a)4−3−1−2b)3 −1− 2 − 4c)1 −3− 4 − 2d)1−3−2−4Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A machine of mass 100 kg is subjected to an external harmonic force with a frequency of 40 rad/s. The designer decides to mount the machine on an isolator to reduce the force transmitted to the foundation. The isolator can be considered as a combination of stiffness ( K) and damper (damping factor, ξ ) in parallel. The designer has the following four isolators:1. K = 640 kN/m, ξ = 0.702. K = 640 kN/m, ξ = 0.073. K = 22.5 kN/m, ξ = 0.704. K = 22.5 kN/m, ξ = 0.07Arrange the isolators in the ascending order of the force transmitted to the foundation.a)4−3−1−2b)3 −1− 2 − 4c)1 −3− 4 − 2d)1−3−2−4Correct answer is option 'A'. Can you explain this answer?.
Solutions for A machine of mass 100 kg is subjected to an external harmonic force with a frequency of 40 rad/s. The designer decides to mount the machine on an isolator to reduce the force transmitted to the foundation. The isolator can be considered as a combination of stiffness ( K) and damper (damping factor, ξ ) in parallel. The designer has the following four isolators:1. K = 640 kN/m, ξ = 0.702. K = 640 kN/m, ξ = 0.073. K = 22.5 kN/m, ξ = 0.704. K = 22.5 kN/m, ξ = 0.07Arrange the isolators in the ascending order of the force transmitted to the foundation.a)4−3−1−2b)3 −1− 2 − 4c)1 −3− 4 − 2d)1−3−2−4Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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Here you can find the meaning of A machine of mass 100 kg is subjected to an external harmonic force with a frequency of 40 rad/s. The designer decides to mount the machine on an isolator to reduce the force transmitted to the foundation. The isolator can be considered as a combination of stiffness ( K) and damper (damping factor, ξ ) in parallel. The designer has the following four isolators:1. K = 640 kN/m, ξ = 0.702. K = 640 kN/m, ξ = 0.073. K = 22.5 kN/m, ξ = 0.704. K = 22.5 kN/m, ξ = 0.07Arrange the isolators in the ascending order of the force transmitted to the foundation.a)4−3−1−2b)3 −1− 2 − 4c)1 −3− 4 − 2d)1−3−2−4Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A machine of mass 100 kg is subjected to an external harmonic force with a frequency of 40 rad/s. The designer decides to mount the machine on an isolator to reduce the force transmitted to the foundation. The isolator can be considered as a combination of stiffness ( K) and damper (damping factor, ξ ) in parallel. The designer has the following four isolators:1. K = 640 kN/m, ξ = 0.702. K = 640 kN/m, ξ = 0.073. K = 22.5 kN/m, ξ = 0.704. K = 22.5 kN/m, ξ = 0.07Arrange the isolators in the ascending order of the force transmitted to the foundation.a)4−3−1−2b)3 −1− 2 − 4c)1 −3− 4 − 2d)1−3−2−4Correct answer is option 'A'. Can you explain this answer?, a detailed solution for A machine of mass 100 kg is subjected to an external harmonic force with a frequency of 40 rad/s. The designer decides to mount the machine on an isolator to reduce the force transmitted to the foundation. The isolator can be considered as a combination of stiffness ( K) and damper (damping factor, ξ ) in parallel. The designer has the following four isolators:1. K = 640 kN/m, ξ = 0.702. K = 640 kN/m, ξ = 0.073. K = 22.5 kN/m, ξ = 0.704. K = 22.5 kN/m, ξ = 0.07Arrange the isolators in the ascending order of the force transmitted to the foundation.a)4−3−1−2b)3 −1− 2 − 4c)1 −3− 4 − 2d)1−3−2−4Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of A machine of mass 100 kg is subjected to an external harmonic force with a frequency of 40 rad/s. The designer decides to mount the machine on an isolator to reduce the force transmitted to the foundation. The isolator can be considered as a combination of stiffness ( K) and damper (damping factor, ξ ) in parallel. The designer has the following four isolators:1. K = 640 kN/m, ξ = 0.702. K = 640 kN/m, ξ = 0.073. K = 22.5 kN/m, ξ = 0.704. K = 22.5 kN/m, ξ = 0.07Arrange the isolators in the ascending order of the force transmitted to the foundation.a)4−3−1−2b)3 −1− 2 − 4c)1 −3− 4 − 2d)1−3−2−4Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A machine of mass 100 kg is subjected to an external harmonic force with a frequency of 40 rad/s. The designer decides to mount the machine on an isolator to reduce the force transmitted to the foundation. The isolator can be considered as a combination of stiffness ( K) and damper (damping factor, ξ ) in parallel. The designer has the following four isolators:1. K = 640 kN/m, ξ = 0.702. K = 640 kN/m, ξ = 0.073. K = 22.5 kN/m, ξ = 0.704. K = 22.5 kN/m, ξ = 0.07Arrange the isolators in the ascending order of the force transmitted to the foundation.a)4−3−1−2b)3 −1− 2 − 4c)1 −3− 4 − 2d)1−3−2−4Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
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