Consider the function $$F\left( s \right) = {5 \over {s\left( {{s^2} + 3s + 2} \right)}}$$ Where $$F(s)$$ is the Laplace transform of the function $$f(t).$$ The initial value of $$f(t)$$ is equal to

A control system is defined by the following mathematical relationship $$${{{d^2}x} \over {d{t^2}}} + 6{{dx} \over {dt}} + 5x = 12\left( {1 - {e^{ - 2t}}} \right)$$$

The response of the system as $$\,t \to \infty $$ is

A unity feedback system has open loop transfer function $$G(s).$$ The steady-state error is zero for

The output of a linear time invariant control system is $$c(t)$$ for a certain input $$r(t).$$ If $$r(t)$$ is modified by passing it through a block whose transfer function is $${e^{ - s}}$$ and then applied to the system, the modified output of the system would be