Question

The input x(t) to a system is related to its output y(t) as

$\frac{dy\left(t\right)}{dt}+y\left(t\right)=3x(t-3)u(t-3)$

Here u(t) represents a unit-step function. The transfer function of this system is ___________ .

• A. $\frac{3e^{-3s}}{s+1}$
• B. $\frac{3e^{-\left(s/3\right)}}{s+1}$
• C. $\frac{e^{-3s}}{s+3}$
• D. $\frac{e^{-\left(s/3\right)}}{s+3}$

Answer 1

The correct option is A $\frac{3e^{-3s}}{s+1}$

$\frac{dy\left(t\right)}{dt}+y\left(t\right)=3x(t-3)$

Taking laplace both sides,

$sY\left(s\right)+Y\left(s\right)=3X\left(s\right)e^{-3s}$

$H\left(s\right)=\frac{Y\left(s\right)}{X\left(s\right)}=\frac{3e^{-3s}}{(s+1)}$