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GATE 2018 ME (ME1) – Question 17

Vibrations · Forced vibration and resonance · 1 mark · Multiple choice

A spring–mass system obeys $M\ddot x+Kx=F\cos(\omega t)$, with mass M, stiffness K, force amplitude F and excitation angular frequency ω. Resonance occurs at ω = ______.

  1. $\sqrt{M/K}$
  2. $\frac1{2\pi}\sqrt{K/M}$
  3. $2\pi\sqrt{K/M}$
  4. $\sqrt{K/M}$

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Show answer and explanation

Correct answer: (D) $\sqrt{K/M}$

Explanation

The undamped system has natural angular frequency $\omega_n=\sqrt{K/M}$. Resonance occurs when excitation angular frequency equals this value (D). The factor 2π converts between angular frequency and cycles per second.