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GATE 2024 ME – Question 25

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

A linear spring-mass-dashpot system with a mass of 2 kg is set in motion with viscous damping. If the natural frequency is 15 Hz, and the amplitudes of two successive cycles measured are 7.75 mm and 7.20 mm, the coefficient of viscous damping (in N.s/m) is

  1. 4.41
  2. 7.51
  3. 2.52
  4. 6.11

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Show answer and explanation

Correct answer: (A) 4.41

Explanation

The logarithmic decrement is $\delta = \ln\frac{7.75}{7.20} = 0.0736$. The damping ratio is $\zeta = \frac{\delta}{\sqrt{4\pi^2 + \delta^2}} = 0.01171$. The natural frequency is $\omega_n = 2\pi \times 15 = 94.25$ rad/s, so $c = 2\zeta m\omega_n = 2 \times 0.01171 \times 2 \times 94.25 = 4.41$ N·s/m.