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GATE 2019 CE (CE1) – Question 13

Structural Analysis · Stiffness matrix method · 1 mark · Multiple choice

A mass m hangs from a spring of stiffness k. With displacement z, its free-vibration equation is $m\ddot z+kz=0$. Find natural frequency as expressed in the choices.

  1. $k/m$
  2. $\sqrt{k/m}$
  3. $m/k$
  4. $\sqrt{m/k}$

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Show answer and explanation

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

Explanation

Divide the equation by m: $\ddot z+(k/m)z=0$. Comparing with $\ddot z+\omega_n^2z=0$ gives $\omega_n=\sqrt{k/m}$: **B**. This is angular frequency; cycles per second require division by $2\pi$.