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An automobile is found to have a natural frequency of 20 rad/s without load and 17.32 rad/s with load of mass 500 kg. The mass of the automobile by treating it as single degree of freedom is......Kg
(Important - Enter only the numerical value in the answer)
Correct answer is between '1499,1500'. Can you explain this answer?
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Verified Answer
An automobile is found to have anatural frequency of 20 rad/swithout l...
m = 1499.6481 Kg
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An automobile is found to have anatural frequency of 20 rad/swithout l...
Given data:
Natural frequency without load, ωn = 20 rad/s
Natural frequency with load, ωn' = 17.32 rad/s
Mass of the load, m = 500 kg
Formula used:
Natural frequency, ωn = √(k/m)
where k is the stiffness of the system.
Calculation:
Let the mass of the automobile be M. Treating it as a single degree of freedom system, the natural frequency with load can be calculated as:
ωn' = √(k/(M+m))
Substituting the given values, we get:
17.32 = √(k/(M+500))
Squaring both sides, we get:
k/(M+500) = 300
k = 300(M+500)
Similarly, the natural frequency without load can be expressed as:
ωn = √(k/M)
Substituting the value of k from the above equation, we get:
20 = √(300(M+500)/M)
Squaring both sides, we get:
400M = 300(M+500)
Solving for M, we get:
M = 1499.33 kg
Therefore, the mass of the automobile by treating it as a single degree of freedom is 1499.33 kg, which falls within the range of 1499-1500 kg.
Natural frequency without load, ωn = 20 rad/s
Natural frequency with load, ωn' = 17.32 rad/s
Mass of the load, m = 500 kg
Formula used:
Natural frequency, ωn = √(k/m)
where k is the stiffness of the system.
Calculation:
Let the mass of the automobile be M. Treating it as a single degree of freedom system, the natural frequency with load can be calculated as:
ωn' = √(k/(M+m))
Substituting the given values, we get:
17.32 = √(k/(M+500))
Squaring both sides, we get:
k/(M+500) = 300
k = 300(M+500)
Similarly, the natural frequency without load can be expressed as:
ωn = √(k/M)
Substituting the value of k from the above equation, we get:
20 = √(300(M+500)/M)
Squaring both sides, we get:
400M = 300(M+500)
Solving for M, we get:
M = 1499.33 kg
Therefore, the mass of the automobile by treating it as a single degree of freedom is 1499.33 kg, which falls within the range of 1499-1500 kg.
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An automobile is found to have anatural frequency of 20 rad/swithout load and 17.32 rad/s withload of mass 500 kg. The mass ofthe automobile by treating it assingle degree of freedom is......Kg(Important - Enter only the numerical value in the answer)Correct answer is between '1499,1500'. Can you explain this answer?
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An automobile is found to have anatural frequency of 20 rad/swithout load and 17.32 rad/s withload of mass 500 kg. The mass ofthe automobile by treating it assingle degree of freedom is......Kg(Important - Enter only the numerical value in the answer)Correct answer is between '1499,1500'. 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 An automobile is found to have anatural frequency of 20 rad/swithout load and 17.32 rad/s withload of mass 500 kg. The mass ofthe automobile by treating it assingle degree of freedom is......Kg(Important - Enter only the numerical value in the answer)Correct answer is between '1499,1500'. 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 An automobile is found to have anatural frequency of 20 rad/swithout load and 17.32 rad/s withload of mass 500 kg. The mass ofthe automobile by treating it assingle degree of freedom is......Kg(Important - Enter only the numerical value in the answer)Correct answer is between '1499,1500'. Can you explain this answer?.
An automobile is found to have anatural frequency of 20 rad/swithout load and 17.32 rad/s withload of mass 500 kg. The mass ofthe automobile by treating it assingle degree of freedom is......Kg(Important - Enter only the numerical value in the answer)Correct answer is between '1499,1500'. 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 An automobile is found to have anatural frequency of 20 rad/swithout load and 17.32 rad/s withload of mass 500 kg. The mass ofthe automobile by treating it assingle degree of freedom is......Kg(Important - Enter only the numerical value in the answer)Correct answer is between '1499,1500'. 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 An automobile is found to have anatural frequency of 20 rad/swithout load and 17.32 rad/s withload of mass 500 kg. The mass ofthe automobile by treating it assingle degree of freedom is......Kg(Important - Enter only the numerical value in the answer)Correct answer is between '1499,1500'. Can you explain this answer?.
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An automobile is found to have anatural frequency of 20 rad/swithout load and 17.32 rad/s withload of mass 500 kg. The mass ofthe automobile by treating it assingle degree of freedom is......Kg(Important - Enter only the numerical value in the answer)Correct answer is between '1499,1500'. Can you explain this answer?, a detailed solution for An automobile is found to have anatural frequency of 20 rad/swithout load and 17.32 rad/s withload of mass 500 kg. The mass ofthe automobile by treating it assingle degree of freedom is......Kg(Important - Enter only the numerical value in the answer)Correct answer is between '1499,1500'. Can you explain this answer? has been provided alongside types of An automobile is found to have anatural frequency of 20 rad/swithout load and 17.32 rad/s withload of mass 500 kg. The mass ofthe automobile by treating it assingle degree of freedom is......Kg(Important - Enter only the numerical value in the answer)Correct answer is between '1499,1500'. Can you explain this answer? theory, EduRev gives you an
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