A unity feedback system has a plant transfer function given by

$G(s)=\frac{50(s^2+10s+49)}{s^2(s+1)}$

a$)$ On the semi$-$log paper provided, plot the asymptotic Bode diagram for $G(s).$ Show all relevant steps. Indicate the relevant slopes on the diagram.

b$)$ From the asymptotic Bode diagram determine the crossover frequencies, the gain margin, and the phase margin. Indicate these values on the diagram clearly.

c$)$ Is the closed$-$loop system stable? Determine the maximum time delay T $($assume $G(s)$ is multiplied by $e^{-T_s})$ the system can tolerate before instability.