Correct Answer - Option 3 : Settling time
The open-loop transfer function of a unity feedback 2nd order system is,
\(G\left( s \right) = \frac{k}{{s\left( {Js + B} \right)}}\;\)
Closed-loop transfer function:
\(H\left( s \right) = \frac{k}{{s\left( {Js + B} \right) + k}}\)
\(H\left( s \right) = \frac{{k/J}}{{{s^2} + \frac{B}{J}s + \frac{k}{J}}}\)
Now, compare it with the standard equation:
\(H\left( s \right) = \frac{{{\omega _n}}}{{{s^2} + 2\xi {\omega _n}s + \omega _n^2}}\)
Now, settling time
\( = \frac{1}{{\xi {\omega _n}}} = \frac{1}{{\frac{B}{{2J}}}} = \frac{{2J}}{B}\)
Hence only settling time is not affected by system gain k.