1
GATE ECE 2007
+2
-0.6
The frequency response of a linear, time-invariant system is given by $$H\left(f\right)\;=\;\frac5{1\;+\;j10\mathrm{πf}}$$ .The step response of the system is:
A
$$5\left(1\;-\;e^{-5t}\right)u\left(t\right)$$
B
$$5\left(1\;-\;e^{-\frac15}\right)u\left(t\right)$$
C
$$\frac15\;\left(1\;-\;e^{-5t}\right)u\left(t\right)$$
D
$$\frac15\;\left(1\;-\;e^{-\frac15}\right)u\left(t\right)$$
2
GATE ECE 2007
+2
-0.6
The transfer function of a plant is $$T\left(s\right)=\frac5{\left(s+5\right)\left(s^2+s+1\right)}$$$The second-order approximation of T (s) using dominant pole concept is: A $$\frac1{\left(s+5\right)\left(s+1\right)}$$ B $$\frac5{\left(s+5\right)\left(s+1\right)}$$ C $$\frac5{\left(s^2+s+1\right)}$$ D $$\frac1{\left(s^2+s+1\right)}$$ 3 GATE ECE 2006 MCQ (Single Correct Answer) +2 -0.6 The unit impulse response of a system is: $$h\left(t\right)\;=\;e^{-t},\;t\geq0$$$ For this system, the steady-state value of the output for unit step input is equal to
A
-1
B
$$0$$
C
1
D
$$\infty$$
4
GATE ECE 2006
+2
-0.6
The unit-step response of a system starting from rest is given by $$\mathrm c\left(\mathrm t\right)=1-\mathrm e^{-2\mathrm t}\;\mathrm{for}\;\mathrm t\geq0$$\$The transfer function of the system is:
A
$$\frac1{1+2s}$$
B
$$\frac2{2+s}$$
C
$$\frac1{2+s}$$
D
$$\frac{2s}{1+2s}$$
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