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GATE 2017 ME (ME2) – Question 16

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

Mass m is attached to two identical springs of constant k as shown. Its natural frequency is ______.

Diagram for GATE 2017 ME (ME2) question 16
  1. $\sqrt{2k/m}$
  2. $\sqrt{k/m}$
  3. $\sqrt{k/(2m)}$
  4. $\sqrt{4k/m}$

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Show answer and explanation

Correct answer: (A) $\sqrt{2k/m}$

Explanation

Both springs experience the same displacement x and exert restoring forces kx. The equivalent stiffness is2k, so the vibration equation is m x-double-dot+2kx=0. Its angular natural frequency is **√(2k/m), A**, measured in radians per second.