Determine the transfer function $$\left( {{{{V_y}} \over {{V_x}}}} \right)$$ for the $$RC$$ network shown in figure $$(1).$$

The network is used as a feedback circuit in an oscillator circuit shown in figure $$(2)$$ to generate sinusoidal oscillations. Assuming that the operational amplifier is ideal, determine the value of $${R_F}$$ for generating these oscillations. Also determine the oscillation frequency if $$R = 10\,\,k\Omega $$ and $$C=100PF$$

The transfer function of the system described by $${{{d^2}y} \over {d{t^2}}} + {{dy} \over {dt}} = {{du} \over {dt}} + 2u$$ with $$u$$ as input and $$y$$ as output is

A unity feedback system has an open loop transfer function, $$G\left( s \right) = {K \over {{s^2}}}.$$ The root locus plot is

The open loop transfer function of a unity feedback system is given by $$G\left( s \right) = {{2\left( {s + \alpha } \right)} \over {s\left( {s + 2} \right)\left( {s + 10} \right)}}.$$ Sketch the root locus as $$\alpha $$ varies from $$0$$ to $$\infty $$. Find the angle and real axis intercept of the asymptotes, breakaway points and the imaginary axis crossing points, if any