Question

The input x(t) and the output y(t) of a linear time invariant system are related as follows :
$y(t)+\frac{dy(t)}{dt}+0.5\frac{d^2y(t)}{dt^2}=x(t)+0.1\frac{dx(t)}{dt}$
What is the Laplace transform of the impulse response of the system ?

• A. $\frac{0.5s^2+s+1}{0.1s+1}$
• B. $\frac{0.1s+1}{0.5s^2+s+1}$
• C. $\frac{0.1s+s^2}{s^2+s+0.5}$
• D. $\frac{s^2+s+0.5}{0.1s^2+s}$

Answer 1

Answer: (B)

$\frac{0.1s+1}{0.5s^2+s+1}$

Answer 2

The correct option is (B) : $\frac{0.1s+1}{0.5s^2+s+1}$.