The positive values of “K” and “a” so that the system shown in the figure below oscillates at a frequency of 2 rad/sec respectively are

The unit-step response of a system starting from rest is given by $$$\mathrm c\left(\mathrm t\right)=1-\mathrm e^{-2\mathrm t}\;\mathrm{for}\;\mathrm t\geq0$$$The transfer function of the system is:

The open-loop transfer function of a unity-gain feedback control system is given by $$G(s) = {K \over {(s + 1)(s + 2)}},$$ the gain margin of the system in dB is given by

In the system shown below, x(t)=(sin t). In steady-state, the response y(t) will be