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GATE 2024 AE – Question 14

Structures · Structural dynamics: free and forced vibration of SDOF systems and free vibration of 2-DOF systems · 1 mark · Multiple choice

Consider the free vibration responses $P$, $Q$, $R$ and $S$ (shown in the figure) of a single degree of freedom spring-mass-damper system with the same initial conditions. For the different damping cases listed below, which one of the following options is correct?

1. Overdamped
2. Underdamped
3. Critically damped
4. Undamped

Displacement against time for four responses with the same start. Q is a sustained oscillation of constant amplitude. R is a decaying oscillation. S is a slow smooth decay without oscillation. P is a fast decay to zero without oscillation (it reaches zero by about t = 2).
  1. P – 1, Q – 4, R – 2, S – 3
  2. P – 1, Q – 2, R – 4, S – 3
  3. P – 3, Q – 4, R – 2, S – 1
  4. P – 3, Q – 2, R – 4, S – 1

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Show answer and explanation

Correct answer: (C) P – 3, Q – 4, R – 2, S – 1

Explanation

An undamped system oscillates forever with a constant amplitude: Q. An underdamped one oscillates with a decaying amplitude: R. The two non-oscillatory curves are the overdamped (slow, sluggish return, S) and the critically damped (the fastest return without overshoot, P).