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

Consider the unit step response of a unity feedback control system whose open loop transfer function is $$G\left( s \right) = {1 \over {s\left( {s + 1} \right)}}.$$ The maximum overshoot is equal to

For a feedback control system of type $$2,$$ the steady state error for a ramp input is

The Laplace transformation of $$f(t)$$ is $$F(s).$$ Given $$F\left( s \right) = {\omega \over {{s^2} + {\omega ^2}}},$$ the final value of $$f(t)$$ is