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GATE 2020 ME (ME1) – Question 16

Vibrations · Vibration isolation and transmissibility ratio · 1 mark · Multiple choice

The single-degree-of-freedom oscillator is subjected to harmonic excitation $F(t)=F_0\cos(\omega t)$ as shown. Find the nonzero ω for which the amplitude of force transmitted to the ground is $F_0$.

Diagram for GATE 2020 ME (ME1) question 16
  1. $\sqrt{k/(2m)}$
  2. $\sqrt{k/m}$
  3. $\sqrt{2k/m}$
  4. $2\sqrt{k/m}$

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

Explanation

Force transmissibility squared is $[1+(2\zeta r)^2]/[(1-r^2)^2+(2\zeta r)^2]$. Setting it to one cancels damping and yields (1−r²)²=1. Apart from r=0, r=√2. Thus **ω=√(2k/m), C**.