Step Response of Critically Damped System

Q. A second -order system has the transfer function $\frac{C\left(s\right)}{R\left(s\right)}=\frac{4}{s^2+4s+4}$. With $r\left(t\right)$ as the unit-step function, the response $c\left(t\right)$ of the system is represented by

1. 
2. 
3. 
4. 

Q. The closed loop transfer function of a control system is given by

$\frac{C\left(s\right)}{R\left(s\right)}=\frac{2(s-1)}{(s+2)(s+1)}$

for a unit step input the output is

1. $-3e^{-2t}+4e^{-t}-1$
2. $-3e^{-2t}-4e^{-t}+1$
3. zero
4. infinity

Q. Consider a casual second-order system will be transfer function
$G\left(s\right)=\frac{1}{1+2s+s^2}$
with a unit-step $R\left(s\right)=\frac{1}{s}$ as an input. Let $C\left(s\right)$ be the corresponding output. The time taken by the system output $c\left(t\right)$ to reach $94\%$ of its steady-state value $\underset{t\to \infty }{lim}c\left(t\right)$, rounded off to two decimal places, is

1. $5.25$
2. $4.50$
3. $2.81$
4. $3.89$