Mechanical Engineering Exam > Mechanical Engineering Questions > If damping coefficient and critical damping c...
Start Learning for Free
If damping coefficient and critical damping coefficient of a vibrating system are 40N/m/s and 416 N/m/s respectively, then the logarithmic decrement is _______.
- a)0.4
- b)0.5
- c)0.6
- d)0.75
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
If damping coefficient and critical damping coefficient of a vibrating...
Most Upvoted Answer
If damping coefficient and critical damping coefficient of a vibrating...
Logarithmic decrement is a measure of the rate at which the amplitude of vibrations in a system decreases over time. It is calculated using the formula:
Logarithmic decrement = ln(A1/A2)
Where A1 is the initial amplitude of vibrations and A2 is the amplitude of vibrations after one complete cycle.
Given that the damping coefficient of the vibrating system is 40 N/m/s and the critical damping coefficient is 416 N/m/s, we can calculate the logarithmic decrement as follows:
Step 1: Calculate the damping factor (ζ)
The damping factor is given by the formula:
ζ = c / (2 * m * ωn)
Where c is the damping coefficient, m is the mass of the system, and ωn is the natural frequency of the system.
Step 2: Calculate the natural frequency (ωn)
The natural frequency is given by the formula:
ωn = √(k / m)
Where k is the stiffness of the system.
Step 3: Calculate the mass (m)
The mass can be calculated using the formula:
m = c / ζ / ωn
Step 4: Calculate the natural frequency (ωn)
Using the stiffness (k) and mass (m), we can calculate the natural frequency using the formula mentioned in Step 2.
Step 5: Calculate the damping factor (ζ)
Using the damping coefficient (c), mass (m), and natural frequency (ωn), we can calculate the damping factor using the formula mentioned in Step 1.
Step 6: Calculate the logarithmic decrement
Using the damping factor (ζ), we can calculate the logarithmic decrement using the formula mentioned at the beginning.
In this case, the damping coefficient is 40 N/m/s and the critical damping coefficient is 416 N/m/s. By comparing these values, we can determine that the system is underdamped.
Therefore, the correct answer is option 'C' (0.6).
Logarithmic decrement = ln(A1/A2)
Where A1 is the initial amplitude of vibrations and A2 is the amplitude of vibrations after one complete cycle.
Given that the damping coefficient of the vibrating system is 40 N/m/s and the critical damping coefficient is 416 N/m/s, we can calculate the logarithmic decrement as follows:
Step 1: Calculate the damping factor (ζ)
The damping factor is given by the formula:
ζ = c / (2 * m * ωn)
Where c is the damping coefficient, m is the mass of the system, and ωn is the natural frequency of the system.
Step 2: Calculate the natural frequency (ωn)
The natural frequency is given by the formula:
ωn = √(k / m)
Where k is the stiffness of the system.
Step 3: Calculate the mass (m)
The mass can be calculated using the formula:
m = c / ζ / ωn
Step 4: Calculate the natural frequency (ωn)
Using the stiffness (k) and mass (m), we can calculate the natural frequency using the formula mentioned in Step 2.
Step 5: Calculate the damping factor (ζ)
Using the damping coefficient (c), mass (m), and natural frequency (ωn), we can calculate the damping factor using the formula mentioned in Step 1.
Step 6: Calculate the logarithmic decrement
Using the damping factor (ζ), we can calculate the logarithmic decrement using the formula mentioned at the beginning.
In this case, the damping coefficient is 40 N/m/s and the critical damping coefficient is 416 N/m/s. By comparing these values, we can determine that the system is underdamped.
Therefore, the correct answer is option 'C' (0.6).
Attention Mechanical Engineering Students!
To make sure you are not studying endlessly, EduRev has designed Mechanical Engineering study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Mechanical Engineering.
|
Explore Courses for Mechanical Engineering exam
|
|
Similar Mechanical Engineering Doubts
Top Courses for Mechanical EngineeringView all
If damping coefficient and critical damping coefficient of a vibrating system are 40N/m/s and 416 N/m/s respectively, then the logarithmic decrement is _______.a)0.4b)0.5c)0.6d)0.75Correct answer is option 'C'. Can you explain this answer?
Question Description
If damping coefficient and critical damping coefficient of a vibrating system are 40N/m/s and 416 N/m/s respectively, then the logarithmic decrement is _______.a)0.4b)0.5c)0.6d)0.75Correct answer is option 'C'. 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 If damping coefficient and critical damping coefficient of a vibrating system are 40N/m/s and 416 N/m/s respectively, then the logarithmic decrement is _______.a)0.4b)0.5c)0.6d)0.75Correct answer is option 'C'. 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 If damping coefficient and critical damping coefficient of a vibrating system are 40N/m/s and 416 N/m/s respectively, then the logarithmic decrement is _______.a)0.4b)0.5c)0.6d)0.75Correct answer is option 'C'. Can you explain this answer?.
If damping coefficient and critical damping coefficient of a vibrating system are 40N/m/s and 416 N/m/s respectively, then the logarithmic decrement is _______.a)0.4b)0.5c)0.6d)0.75Correct answer is option 'C'. 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 If damping coefficient and critical damping coefficient of a vibrating system are 40N/m/s and 416 N/m/s respectively, then the logarithmic decrement is _______.a)0.4b)0.5c)0.6d)0.75Correct answer is option 'C'. 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 If damping coefficient and critical damping coefficient of a vibrating system are 40N/m/s and 416 N/m/s respectively, then the logarithmic decrement is _______.a)0.4b)0.5c)0.6d)0.75Correct answer is option 'C'. Can you explain this answer?.
Solutions for If damping coefficient and critical damping coefficient of a vibrating system are 40N/m/s and 416 N/m/s respectively, then the logarithmic decrement is _______.a)0.4b)0.5c)0.6d)0.75Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning of If damping coefficient and critical damping coefficient of a vibrating system are 40N/m/s and 416 N/m/s respectively, then the logarithmic decrement is _______.a)0.4b)0.5c)0.6d)0.75Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If damping coefficient and critical damping coefficient of a vibrating system are 40N/m/s and 416 N/m/s respectively, then the logarithmic decrement is _______.a)0.4b)0.5c)0.6d)0.75Correct answer is option 'C'. Can you explain this answer?, a detailed solution for If damping coefficient and critical damping coefficient of a vibrating system are 40N/m/s and 416 N/m/s respectively, then the logarithmic decrement is _______.a)0.4b)0.5c)0.6d)0.75Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of If damping coefficient and critical damping coefficient of a vibrating system are 40N/m/s and 416 N/m/s respectively, then the logarithmic decrement is _______.a)0.4b)0.5c)0.6d)0.75Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If damping coefficient and critical damping coefficient of a vibrating system are 40N/m/s and 416 N/m/s respectively, then the logarithmic decrement is _______.a)0.4b)0.5c)0.6d)0.75Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
|
|
Explore Courses for Mechanical Engineering exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup