A non inverting op - amp amplifier is shown in figure. The o/p voltage is

Let the magnitude of the gain in the inverting op - amp amplifier circuit shown be $$x$$ with switch $${S_1}$$ open. When the switch $${S_1}$$ is closed, the magnitude of gain becomes.

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

For the system shown in Figure, with a damping ratio $$\xi $$ of $$0.7$$ and an undamped natural frequency $${\omega _n}$$ of $$4$$ rad/sec, the values of $$' K '$$ and $$' a '$$ are