Question

For the following system,


when $X_1\left(s\right)=0$, the transfer function $\frac{Y\left(s\right)}{X_2\left(s\right)}$ is

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

Answer 1

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

Redrawing the block diagram with $X_1\left(s\right)=0$


The transfer function
$T\left(s\right)=\frac{Y\left(s\right)}{X_2\left(s\right)}=\frac{G\left(s\right)}{1+G\left(s\right)H\left(s\right)}.....\left(i\right)$
$Here,G\left(s\right)=\frac{1}{s}andH\left(s\right)=\frac{s}{s+1}$

$\frac{Y\left(s\right)}{X_2\left(s\right)}=\frac{1/s}{1+\frac{1}{s}\times \frac{s}{s+1}}=\frac{(s+1)}{s(s+2)}$