(Solved): 1. (18 pts) A system is represented by the following transfer function \[ G(s)=\frac{Y(s)}{U(s)}=\f ...

1. (18 pts) A system is represented by the following transfer function \[ G(s)=\frac{Y(s)}{U(s)}=\frac{84}{\left(3 s^{2}+21 s+36\right)\left(s^{2}+2 s+9\right)} \] The input is a step function \( u(t)=5 U(t) \). (a) Show that the system is stable. (b) Determine the steady-state output. (c) Determine the settling time to reach steady state.