1
GATE EE 2014 Set 2
+1
-0.3
Consider an LTI system with transfer function $$H\left(s\right)=\frac1{s\left(s+4\right)}$$.If the input to the system is cos(3t) and the steady state output is $$A\sin\left(3t+\alpha\right)$$, then the value of A is
A
1/30
B
1/15
C
3/4
D
4/3
2
GATE EE 2014 Set 1
+1
-0.3
x(t) is nonzero only for $$T_x\;<\;t\;<\;T_x^1$$ , and similarly, y(t) is nonzero only for $$T_y\;<\;t\;<\;T_y^1$$ . Let z(t) be convolution of x(t) and y(t). Which one of the following statements is TRUE?
A
z(t) can be nonzero over an unbounded interval
B
z(t) is nonzero for $$t\;<\;T_x+T_y$$
C
z(t) is zero outside of $$T_x+T_y\;<\;t\;<\;T_x^1+T_y^1$$
D
z(t) is nonzero for $$t\;>\;T_x^1+T_y^1$$
3
GATE EE 2013
+1
-0.3
The impulse response of a system is h(t) = tu(t). For an input u(t − 1), the output is
A
$$\frac{t^2}2u\left(t\right)$$
B
$$\frac{t\left(t-1\right)}2u\left(t-1\right)$$
C
$$\frac{\left(t-1\right)^2}2u\left(t-1\right)$$
D
$$\frac{t^2-1}2u\left(t-1\right)$$
4
GATE EE 2013
+1
-0.3
Assuming zero initial condition, the response y(t) of the system given below to a unit step input u(t) is
A
u(t)
B
tu(t)
C
$$\frac{t^2}2u\left(t\right)$$
D
$$e^{-t}u\left(t\right)$$
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