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In vibration isolation system, if ω/ωn is less than √2, then for all values of the damping factor, the transmissibility will be
where ω = Circular frequency of the system in rad/s, and ωn = Natural circular frequency of vibration of the system in rad/s.
- a)less than unity
- b)equal to unity
- c)greater than unity
- d)zero
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
In vibration isolation system, if ω/ωn is less than √2, then for all ...
The value of ω / ωn must be greater than √2 if ε is to be less than 1 and it is the numerical value of ε, independent of any phase difference between the forces that may exist which is important.
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In vibration isolation system, if ω/ωn is less than √2, then for all ...
Explanation:
Transmissibility is defined as the ratio of amplitude of vibration of the system at the point of interest to the amplitude of the excitation force applied to the system. It is expressed as the ratio of the amplitude of the output to the amplitude of the input.
Transmissibility (TR)= (Amplitude of output vibration) / (Amplitude of input force)
The transmissibility of a vibration isolation system is given by the following equation:
TR = 1 / [(1- (ω/ωn)^2) + (2ζω/ωn)^2]^0.5
where ω = Circular frequency of the system in rad/s, ωn = Natural circular frequency of vibration of the system in rad/s, and ζ = Damping ratio of the system.
If ω/ωn is less than √2, then for all values of the damping factor, the transmissibility will be greater than unity. This can be explained as follows:
1. When ω/ωn < √2,="" the="" denominator="" of="" the="" transmissibility="" equation="" is="" greater="" than="" one,="" which="" means="" that="" the="" value="" of="" tr="" is="" less="" than="" />
2. As the damping factor ζ increases, the value of TR decreases.
3. However, even for the highest value of damping factor ζ, the value of TR will still be greater than one if ω/ωn < />
4. This means that the amplitude of vibration at the point of interest will be greater than the amplitude of the excitation force applied to the system.
5. This condition is known as resonance, and it occurs when the frequency of the excitation force is close to the natural frequency of the system.
6. Resonance can lead to excessive vibration amplitudes and can cause damage to the system.
7. Therefore, it is important to design vibration isolation systems such that the natural frequency of the system is well separated from the excitation frequency.
In summary, if ω/ωn is less than √2, then for all values of the damping factor, the transmissibility will be greater than unity, which can lead to resonance and excessive vibration amplitudes.
Transmissibility is defined as the ratio of amplitude of vibration of the system at the point of interest to the amplitude of the excitation force applied to the system. It is expressed as the ratio of the amplitude of the output to the amplitude of the input.
Transmissibility (TR)= (Amplitude of output vibration) / (Amplitude of input force)
The transmissibility of a vibration isolation system is given by the following equation:
TR = 1 / [(1- (ω/ωn)^2) + (2ζω/ωn)^2]^0.5
where ω = Circular frequency of the system in rad/s, ωn = Natural circular frequency of vibration of the system in rad/s, and ζ = Damping ratio of the system.
If ω/ωn is less than √2, then for all values of the damping factor, the transmissibility will be greater than unity. This can be explained as follows:
1. When ω/ωn < √2,="" the="" denominator="" of="" the="" transmissibility="" equation="" is="" greater="" than="" one,="" which="" means="" that="" the="" value="" of="" tr="" is="" less="" than="" />
2. As the damping factor ζ increases, the value of TR decreases.
3. However, even for the highest value of damping factor ζ, the value of TR will still be greater than one if ω/ωn < />
4. This means that the amplitude of vibration at the point of interest will be greater than the amplitude of the excitation force applied to the system.
5. This condition is known as resonance, and it occurs when the frequency of the excitation force is close to the natural frequency of the system.
6. Resonance can lead to excessive vibration amplitudes and can cause damage to the system.
7. Therefore, it is important to design vibration isolation systems such that the natural frequency of the system is well separated from the excitation frequency.
In summary, if ω/ωn is less than √2, then for all values of the damping factor, the transmissibility will be greater than unity, which can lead to resonance and excessive vibration amplitudes.
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In vibration isolation system, if ω/ωn is less than √2, then for all values of the damping factor, the transmissibility will bewhere ω = Circular frequency of the system in rad/s, and ωn = Natural circular frequency of vibration of the system in rad/s.a)less than unityb)equal to unityc)greater than unityd)zeroCorrect answer is option 'C'. Can you explain this answer?
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In vibration isolation system, if ω/ωn is less than √2, then for all values of the damping factor, the transmissibility will bewhere ω = Circular frequency of the system in rad/s, and ωn = Natural circular frequency of vibration of the system in rad/s.a)less than unityb)equal to unityc)greater than unityd)zeroCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about In vibration isolation system, if ω/ωn is less than √2, then for all values of the damping factor, the transmissibility will bewhere ω = Circular frequency of the system in rad/s, and ωn = Natural circular frequency of vibration of the system in rad/s.a)less than unityb)equal to unityc)greater than unityd)zeroCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In vibration isolation system, if ω/ωn is less than √2, then for all values of the damping factor, the transmissibility will bewhere ω = Circular frequency of the system in rad/s, and ωn = Natural circular frequency of vibration of the system in rad/s.a)less than unityb)equal to unityc)greater than unityd)zeroCorrect answer is option 'C'. Can you explain this answer?.
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