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A simple spring – mass vibrating system has a natural frequency of ‘ωn’. If the spring stiffness is halved and the mass is doubled, then the natural frequency will become

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  1. ωn / 2
  2. 2ωn
  3. 4ωn
  4. 8ωn

Answer (Detailed Solution Below)

Option 1 : ωn / 2
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Detailed Solution

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Concept: Consider a spring-mass system

 

Natural frequency for a spring mass system is

Calculation:

If stiffness is halved and mass is doubled then

Given: k2 = k1/2, m2 = 2m1

∴ the natural frequency will become ωn / 2

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