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A vibrating system having a mass of 30 kg is supported by 4 springs, each having a stiffness of k. The system runs at 420 rpm. If only 10% of the shaking force is allowed to be transmitted to the supporting structure, then the value of stiffness k will be close to:

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HPCL Engineer Mechanical 04 Nov 2022 Official Paper (Shift 2)
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  1. 1.09 N/mm
  2. 3.96 N/mm
  3. 2.18 N/mm 
  4. 1.32 N/mm

Answer (Detailed Solution Below)

Option 4 : 1.32 N/mm
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Detailed Solution

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Concept:

  • Transmissibility is defined as the ratio of force transmitted to the shaking force. 

Where, Ft = Transmitted force, Fo= Shaking force

Calculation:

Given:

m = 30 kg,

N = 420 rpm ⇒ω = = 43.982 rad/s. 

As no damper is used, ζ = 0

since, 

The springs will be in parallel so, Keq. = 4K

∴   

For zero damping the Transmissibility equation gets reduced to, 

K = 1316.718 N/m = 1.316 N/mm. ≈ 1.32 N/mm.

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