GATE ME 2021 Set 2 — Question 43
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Theory of Machines & Vibrations → Forced Vibration → Magnification & Transmissibility
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Question
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 () and damper (damping factor, ) in parallel. The designer has the following four isolators:1)
2)
3)
4) Arrange the isolators in the ascending order of the force transmitted to the foundation.
2)
3)
4) Arrange the isolators in the ascending order of the force transmitted to the foundation.
Correct answer
(C) 4-3-1-2
Solution
Transmissibility , where and .
Given , .
Isolators 1 & 2: .
Since , higher damping decreases slightly but here is small. Let's calculate:
, . So .
Isolators 3 & 4: .
Since , higher damping increases .
, . So .
Comparing all: .
Ascending order of force transmitted: 4-3-1-2.
Given , .
Isolators 1 & 2: .
Since , higher damping decreases slightly but here is small. Let's calculate:
, . So .
Isolators 3 & 4: .
Since , higher damping increases .
, . So .
Comparing all: .
Ascending order of force transmitted: 4-3-1-2.
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