The GATE Grind

GATE 2018 ME (ME2) – Question 17

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

An additional damper is placed in parallel in the shown underdamped single-degree-of-freedom spring–mass–damper system. The system remains underdamped. Which is ALWAYS true?

Diagram for GATE 2018 ME (ME2) question 17
  1. Transmissibility increases.
  2. Transmissibility decreases.
  3. Time period of free oscillations increases.
  4. Time period of free oscillations decreases.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) Time period of free oscillations increases.

Explanation

The undamped natural frequency $\omega_n=\sqrt{K/M}$ is unchanged. Adding a parallel damper increases damping ratio ζ. While ζ remains below one, $\omega_d=\omega_n\sqrt{1-\zeta^2}$ decreases, so period $2\pi/\omega_d$ increases. Transmissibility depends on excitation frequency and is not universally increasing or decreasing. Answer **C**.