Fig.1, shows the block diagram representation of a control system. The system in block A has an impulse response $${h_A}(t) = {e^{ - t}}\,u(t)$$. The system in block B has an impulse response $${h_B}(t) = {e^{ - 2t}}\,u(t)$$. The block 'k' amplifies its input by a factor k. For the overall system with input x(t) and output y(t)

(a) Find the transfer function $${{Y(s)} \over {X(s)}}$$, when k=1

(b) Find the impulse response, when k = 0

(c) Find the value of k for which the system becomes unstable.

$$$\left[ {\matrix{ {Note:u(t)\, \equiv \,0} & {t\, \le \,0} \cr {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \equiv 1} & {t\, > \,0} \cr } } \right]$$$