1
GATE ECE 2004
+2
-0.6
A causal system having the transfer function $$G\left(s\right)\;=\;\frac1{s\;+\;2}$$ is excited with 10u(t). The time at which the output reaches 99% of its steady state value is
A
2.7 sec
B
2.5 sec
C
2.3 sec
D
2.1 sec
2
GATE ECE 2004
+2
-0.6
A system described by the following differential equation $$\frac{d^2y}{dt^2}+3\frac{dy}{dt}+2y=x\left(t\right)$$\$ is initially at rest. For input x(t) = 2u(t), the output y(t) is
A
$$\left(1-2e^{-t}+e^{-2t}\right)u\left(t\right)$$
B
$$\left(1+2e^{-t}-2e^{-2t}\right)u\left(t\right)$$
C
$$\left(0.5+e^{-t}+1.5e^{-2t}\right)u\left(t\right)$$
D
$$\left(0.5+2e^{-t}+2e^{-2t}\right)u\left(t\right)$$
3
GATE ECE 2003
+2
-0.6
A second-order system has the transfer function $$\frac{C\left(s\right)}{R\left(s\right)}=\frac4{s^2+4s+4}$$. With r(t) as the unit-step function, the response c(t) of the system is represented by
A
B
C
D
4
GATE ECE 2002
+2
-0.6
The transfer function of a system is $$G\left(s\right)\;=\;\frac{100}{\left(s\;+\;1\right)\left(s\;+\;100\right)}$$.For a unit step input to the system the approximate settling time for 2% criterion is
A
100 sec
B
4 sec
C
1 sec
D
0.01 sec
EXAM MAP
Medical
NEET