Basics of Time Response Analysis

Q. The final value theorem is used to find the

1. steady state value of the system output
2. initial value of the system output
3. transient behavior of the system output
4. none of these

Q. The transfer function of a plant is
$T\left(s\right)=\frac{5}{(s+5)(s^2+s+1)}.$ The second-order approximation of $T\left(s\right)$ using dominant pole concept is

1. $\frac{1}{(s+5)(s+1)}$
2. $\frac{5}{(s+5)(s+1)}$
3. $\frac{5}{s^2+s+1}$
4. $\frac{1}{s^2+s+1}$

Q. If $L\left[f\right(t\left)\right]=\frac{2(s+1)}{s^2+2s+5}$ then $f\left(0^{+}\right)$ and $f\left(\infty \right)$ are given by

1. $0,2$ respectively
2. $2,0$ respectively
3. $0,1$ respectively
4. $2/5,0$ respectively

Q. The system $G\left(s\right)=\frac{0.8}{s^2+s-2}$ is subjected to step input. The system output y(t) at $t\to \infty$, is

1. 0.8
2. 0.4
3. -0.4
4. unbounded