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GATE 2019 ME (ME1) – Question 16

Vibrations · Free vibration of single degree of freedom systems, damping · 1 mark · Multiple choice

The spring–mass systems I and II shown have natural frequencies $\omega_I$ and $\omega_{II}$. Find their ratio $\omega_I/\omega_{II}$.

Diagram for GATE 2019 ME (ME1) question 16
  1. 1/4
  2. 1/2
  3. 2
  4. 4

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Correct answer: (B) 1/2

Explanation

Series stiffness is $k_s=(1/k+1/k)^{-1}=k/2$; parallel stiffness is 2k. Since $\omega_n=\sqrt{k_{eq}/M}$, the ratio is $\sqrt{(k/2)/(2k)}=1/2$. **Answer: B**. The mass is identical and cancels.