Question

What is the impulse response y(t) of a system with transfer function $\frac{Y\left(s\right)}{R\left(s\right)}=\frac{1}{(s+1)(s+10)}$

• A. y(t) =$\frac{1}{9}{e}^{-t}+\frac{1}{9}{e}^{-10t}$
• B. y(t) =$\frac{1}{9}{e}^{-t}-\frac{1}{9}{e}^{-10t}$
• C. y(t)$=e^{-t}-e^{-10t}$
• D. y(t)$=e^{-t}+e^{-10t}$

Answer 1

The correct option is B y(t) =$\frac{1}{9}{e}^{-t}-\frac{1}{9}{e}^{-10t}$

For impulse response, R(s) = 1
The impulse response is given by,

$y\left(t\right)=L^{-1}\left\{\frac{1}{(s+1)(s+10)}\right\}$
$y\left(t\right)=L^{-1}\{\frac{1}{9(s+1)}-\frac{1}{9(s+10)}\}$

y(t) =$\frac{1}{9}{e}^{-t}-\frac{1}{9}{e}^{-10t}$