Match the following:   Curve   Nature of damping I Curve (a) A Un - Damped II Curve (b) B Over Damped III Curve (c) C Under Damped IV Curve (d) D Critically Damped

Match the following:   Curve   Nature of damping I Curve (a) A Un - Damped II Curve (b) B Over Damped III Curve (c) C Under Damped IV Curve (d) D Critically Damped Correct Answer I - D, II - C, III - B, IV - A

Damping Ratio, ξ = c/cc

ξ = 0: Undamped System

ξ > 1: Over Damped System

ξ < 1: Under Damped System

ξ = 1: Critically Damped System

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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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