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Which of the following diagrams represents the response of a critically damped (ξ = 1) SDOF system to initial conditions?

Which of the following diagrams represents the response of a critically damped (ξ = 1) SDOF system to initial conditions? Correct Answer <img alt="F1 Shubhanshi Ravi 16.10.21 D38" src="//storage.googleapis.com/tb-img/production/21/10/F1_Shubhanshi_Ravi_16.10.21_D38.png" style="width: 433px; height: 300px;">

Explanation:

Damping Ratio, ξ = c/cc

ξ = 0: Undamped System

ξ > 1: Over Damped System

ξ < 1: Under Damped System

ξ = 1: Critically Damped System

Important Points

[ alt="F2 S.S-D.K 05.09.2019 D1" src="//storage.googleapis.com/tb-img/production/19/09/F2_S.S-D.K_05.09.2019_D1.png" style="width: 365px; height: 177px;">

Overdamped System: ζ > 1

This is the equation of aperiodic motion i.e. the system cannot vibrate due to over-damping. The magnitude of the resultant displacement approaches zero with time.

Underdamped: ζ < 1

This resultant motion is oscillatory with decreasing amplitudes having a frequency of ωd. Ultimately, the motion dies down with time.

Critical Damping: ζ = 1

The displacement will be approaching to zero with shortest possible time.

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