$($a$)$ Using the nyquist plot, find the range of T $0$ in which the above system is stable.

$($b$)$ Find the range of T$>0$ where the size of the gain margin becomes larger than $3.$

$($c$)$ When T$=0\mathrm{.}5,$ express the transfer function of the closed loop system as a rational polynomial using the pade approximation of the first order.

don't use matlab program.