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For a critically damped second order system, if gain constant (K) is increased, the system behaviour 

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  1. becomes oscillatory
  2. becomes under damped
  3. becomes over damped 
  4. shows no change 

Answer (Detailed Solution Below)

Option 2 : becomes under damped
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Detailed Solution

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Concept:

We know that for second-order system damping ratio

\(ζ = \frac{1}{{\surd K}}\)

K = gain constant

Now for a critically damped system if we increase gain constant K then decreases in damping ratio

K ↑ → ζ ↓ 

then system behaviour becomes underdamped

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