A system has a transfer function of $\frac{Y(s)}{R(s)}=\frac{s(3s+6)}{9s^2+5s+9}.$

Assuming $Y(s)$ is stable, determine

a$)$ the final value of $y(t)$ if the input $R(s)$ is a unit ramp

b$)$ the final value of $y(t)$ if the input $R(s)$ is a unit step

c$)$ the initial value of $y(t)$ if the input $R(s)$ is a unit step