Question

A linear time invariant system initially at rest, when subjected to a unit step input, gives a response $y\left(t\right)=t{e}^{-t},t>0$. The transfer function of the system is

• A. $\frac{1}{(s+1{)}^2}$
• B. $\frac{1}{s(s+1{)}^2}$
• C. $\frac{s}{(s+1{)}^2}$
• D. $\frac{1}{s(s+1)}$

Answer 1

The correct option is C $\frac{s}{(s+1{)}^2}$

$X\left(s\right)=L\left(u\right(t\left)\right)=\frac{1}{s}$
$Y\left(s\right)=L\left(t{e}^{-t}\right)=\frac{1}{(s+1{)}^2}$
$\therefore T.F=\frac{Y\left(s\right)}{X\left(s\right)}=\frac{s}{(s+1{)}^2}$