1
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 $$\left(0.5+2e^{-t}+2e^{-2t}\right)u\left(t\right)$$ 2 GATE ECE 2003 MCQ (Single Correct Answer) +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 3 GATE ECE 2002 MCQ (Single Correct Answer) +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 4 GATE ECE 1999 MCQ (Single Correct Answer) +2 -0.6 If the closed-loop transfer function T(s) of a unity negative feedback system is given by $$T\left(s\right)=\frac{a_{n-1}s+a_n}{s^n+a_1s^{n-1}+.....+a_{n-1}s+a_n}$$$ then the steady state error for a unit ramp input is
A
$$\frac{a_n}{a_{n-1}}$$
B
$$\frac{a_n}{a_{n-2}}$$
C
$$\frac{a_{n-2}}{a_{n-2}}$$
D
zero
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