The depletion region (or) space charge region (or) transition region in a semiconductor $$p-n$$ junction diode has

The unit impulse response of a system is given as $$c\left( t \right) = - 4{e^{ - t}} + 6{e^{ - 2t}}.\,\,\,$$ The step response of the same system for $$\,t \ge 0$$ is equal to

The unit - impulse response of a unity - feedback control system is given by $$c\left( t \right) = - t{e^{ - t}} + 2\,\,{e^{ - t}},\,\left( {t \ge 0} \right)$$ the open loop transfer function is equal to

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