Definition of Transfer Function

Q. The transfer function of a Zero-Order-Hold system with sampling interval T is

1. $\frac{1}{s}(1-e^{-Ts})$
2. $\frac{1}{s}(1-e^{-Ts}{)}^2$
3. $\frac{1}{s}{e}^{-Ts}$
4. $\frac{1}{s^2}{e}^{-Ts}$

Q. A linear time invariant system initially at rest, when subjected to a unit step input, gives a response $y\left(t\right)=t{e}^{-t},t>0$. The transfer function of the system is

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

Q. For the system shown in below figure, what is the transfer function $\frac{V_o\left(s\right)}{V_i\left(s\right)}$?

(Given $R_1=R_2=C_1=C_2=1unit$)

1. $\frac{V_o\left(s\right)}{V_i\left(s\right)}=\frac{s}{s^2+3s+1}$
2. $\frac{V_o\left(s\right)}{V_i\left(s\right)}=\frac{1}{s^2+3s+1}$
3. $\frac{V_o\left(s\right)}{V_i\left(s\right)}=\frac{s^2}{s^2+2s+1}$
4. $\frac{V_o\left(s\right)}{V_i\left(s\right)}=\frac{s+1}{s^2+2s+1}$

Q. For a tachometer, if $\theta \left(t\right)$ is the rotor displacement in radians, $e\left(t\right)$ is the output voltage and $K_t$ is the tachometer constant in $V/rad/sec$, then the transfer function,
$\frac{E\left(s\right)}{Q\left(s\right)}$ will be

1. $K_t{s}^2$
2. $\frac{K_t}{s}$
3. $K_{t}s$
4. $K_t$

Q. For the system governed by the set of equation:
$\frac{d{x}_1}{dt}=2x_1+x_2+u$
$\frac{d{x}_2}{dt}=-2x_1+u$
$y=3x_1$
The transfer function $\frac{Y\left(s\right)}{U\left(s\right)}$ is given by

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

Q. The output y(t) of a system is related to its input x(t) as
$y\left(t\right)={\int }_0^{t}x(\tau -2)d\tau$
where, x(t) = 0 and y(t) = 0 for t $\le$ 0. The transfer function of the system is

1. $\frac{1}{s}$
2. $\frac{(1-e^{-2s})}{s}$
3. $\frac{e^{-2s}}{s}$
4. $\frac{1}{s}-e^{-2s}$

Q. The transfer function of the system described by $\frac{d^{2}y}{d{t}^2}+\frac{dy}{dt}=\frac{du}{dt}+2u$ with u as input and y as output is

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