1
GATE EE 2004
+1
-0.3
Consider the function $$F\left( s \right) = {5 \over {s\left( {{s^2} + 3s + 2} \right)}}$$ Where $$F(s)$$ is the Laplace transform of the function $$f(t).$$ The initial value of $$f(t)$$ is equal to
A
$$5$$
B
$$5/2$$
C
$$5/3$$
D
$$0$$
2
GATE EE 2004
+1
-0.3
Consider the function $$F\left( s \right) = {5 \over {s\left( {{s^2} + 3s + 2} \right)}}$$ Where $$F(s)$$ is the Laplace transform of the function $$f(t).$$ The initial value of $$f(t)$$ is equal to
A
$$5$$
B
$$5/2$$
C
$$5/3$$
D
$$0$$
3
GATE EE 2004
+2
-0.6
The block diagram of a closed loop control system is given by figure. The values of $$K$$ and $$P$$ such that the system has a damping ratio of $$0.7$$ and an undamped natural frequency $${\omega _n}$$ of $$5$$ rad/sec, are respectively equal to A
$$20$$ and $$0.3$$
B
$$20$$ and $$0.2$$
C
$$25$$ and $$0.3$$
D
$$25$$ and $$0.2$$
4
GATE EE 2004
+2
-0.6
The unit impulse response of a second order under-damped system starting from rest is given by $$c\left( t \right) = 12.5{e^{ - 6t}}\,\sin 8t,\,\,t \ge 0.$$
The steady-state value of the unit step response of the system is equal to
A
$$0$$
B
$$0.25$$
C
$$0.5$$
D
$$1.0$$
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