The open-loop transfer function of a control system is as follows:

Determine the value of \(k\) so that the closed-loop system has an underdamped response to a unit step input. Moreover, determine the damping ratio of the system response.

1) \(k>\frac{1}{4 \tau}, \xi=\frac{1}{2 \sqrt{\tau k}}\)
2) \(k3) \(k>\frac{1}{4 \tau}, \xi=\frac{1}{2 \tau \sqrt{k}}\)
4) \(k

G(s) = k s(TS+1)