Consider the unit$-$feedback system whose open$-$loop transfer function is

$G(s)=\frac{as+1}{s^2}$

Determine the value of $a$ so that the phase margin is $45.$

Select one:

a$.a=\frac{1}{\sqrt[3]{2}}$

b$.,a=\frac{1}{\sqrt[4]{2}}$

c$.a=\frac{1}{\sqrt[\phantom{2}]{2}}$

d$.a=\frac{\sqrt[3]{2}}{2}$

e$.a=\frac{\sqrt[4]{2}}{2}$