1
GATE ECE 2005
+2
-0.6
In the derivation of expression for peak percent overshoot,$$M_p=exp\left(\frac{-\mathrm{πξ}}{\sqrt{1-\xi^2}}\right)\times100\%$$$.Which one of the following conditions is NOT required? A System is linear and time invariant. B The system transfer function has a pair of complex conjugate poles and no zeroes. C There is no transportation delay in the system. D The system has zero initial conditions. 2 GATE ECE 2004 MCQ (Single Correct Answer) +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 3 GATE ECE 2004 MCQ (Single Correct Answer) +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
$$\left(0.5+2e^{-t}+2e^{-2t}\right)u\left(t\right)$$
4
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
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