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

For a tachometer if $$\theta \left( t \right)$$ is the rotor displacement is radians, $$e\left( t \right)$$ is the output voltage and $${K_t}$$ is the tachometer constant in V/rad/sec, then the transfer function $${{E\left( s \right)} \over {\theta \left( s \right)}},$$ will be

The block diagram of a closed loop control system is given by figure. The values of $$K$$ and $$P$$ such that the system has a damping ratio of $$0.7$$ and an undamped natural frequency $${\omega _n}$$ of $$5$$ rad/sec, are respectively equal to

The Nyquist plot of loop transfer function $$G(s) H(s)$$ of a closed loop control system passes through the point $$(-1,j0)$$ in the $$G(s) H(s)$$ plane. The phase margin of the system is