For the system shown in Figure, with a damping ratio $$\xi $$ of $$0.7$$ and an undamped natural frequency $${\omega _n}$$ of $$4$$ rad/sec, the values of $$' K '$$ and $$' a '$$ are
A
$$K = 4,a = 0.35$$
B
$$K = 8,a = 0.455$$
C
$$K = 16,a = 0.225$$
D
$$K = 64,a = 0.9$$
2
GATE EE 1996
MCQ (Single Correct Answer)
The unit impulse response of a system is given as $$c\left( t \right) = - 4{e^{ - t}} + 6{e^{ - 2t}}.\,\,\,$$ The step response of the same system for $$\,t \ge 0$$ is equal to
A
$$ - 3{e^{ - 2t}} - 4{e^{ - t}} + 1$$
B
$$ - 3{e^{ - 2t}} + 4{e^{ - t}} - 1$$
C
$$ - 3{e^{ - 2t}} - 4{e^{ - t}} - 1$$
D
$$ 3{e^{ - 2t}} + 4{e^{ - t}} - 1$$
3
GATE EE 1991
Fill in the Blanks
A first order system and its response to a unit step input are shown in Fig. below. The system parameters are
$$a=$$ ____________
$$K=$$ ___________
Answer
$$a=5$$
$$K=10$$
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