The polar plot of a type-$$1, 3$$-pole, open-loop system is shown in Fig. below. The closed loop system is

The closed - loop transfer function of a control system is given by $${{C\left( s \right)} \over {R\left( s \right)}} = {1 \over {\left( {1 + s} \right)}}$$
For the input $$\,r\left( t \right)\,\, = \,\,\sin \,t,$$ the steady state value of $$c(t)$$ is equal to

A unity feedback system has the open loop transfer function $$G\left( s \right) = {1 \over {\left( {s - 1} \right)\left( {s + 2} \right)\left( {s + 3} \right)}}$$
The Nyquist plot of $$G$$ encircle the origin

The system having the Bode magnitude plot shown in Fig. below has the transfer function