GATE EC 2006 Set 1 Q83 — Control Systems

Statement for Linked Answer Questions 82 and 83
Consider a unity-gain feedback control system whose open-loop transfer function is
$$G(s)=\frac{as+1}{s^{2}}$$

With the value of '$a$' set for a phase-margin of $\frac{\pi}{4}$, the value of unit-impulse response of the open-loop system at $t=1$ second is equal to