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For a single degree of freedom viscous damped system, if the frequency ratio is greater than √2, it implies that:

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HPCL Engineer Mechanical 04 Nov 2022 Official Paper (Shift 2)
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  1. the transmitted force is more than the exciting force
  2. the transmitted force is equal to the exciting force
  3. the transmitted force is less than the exciting force
  4. the transmitted force is infinite 

Answer (Detailed Solution Below)

Option 3 : the transmitted force is less than the exciting force
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Detailed Solution

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Concept:

Machine transmissibility,

Machine transmissibility depends upon 'ω /ωn'→ (within the machine) = q (say)

​

ζ = Damping factor

Damping is beneficial up to a ratio of 

Whereas no need for damping, less damping, If the ratio of

Explanation:

  • For all the value of the damping ratio, the transmissibility is less than one when the ratio of natural and forced frequency is greater than root 2 or 

⇒ 

  • For all the value of damping ratio, the transmissibility is greater than one when the ratio of natural and forced frequency is less than root 2 and here the chances of getting infinite frequency is also there when the ratio will be 1, so we have to provide damping here only.

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