The transfer function of a tachometer is of the form

The characteristic equation of a feedback control system is $$$s^4+20s^3+15s^2+2s+K\;=\;0$$$
(i) Determine the range of K for the system to be stable.
(ii) Can the system be marginally stable? If so, find the required value of K and the frequency of sustained oscillation.

Consider the system shown in Fig. Determine the value of 'a' such that the damping ratio is 0.5. Also obtain the values of the rise time 't_r' and maximum overshoot 'M_p' in its step response.

Draw a signal flow graph for the following set of algebraic equations: $$$\begin{array}{l}y_2=ay_1-\;gy_3\\y_3=ey_2+\;cy_4\\y_4=by_2-dy_4\end{array}$$$ Hence, find the gains $$\frac{y_2}{y_1}$$ and $$\frac{y_3}{y_1}$$.