GATE EC 2013 Question Paper (10-Feb-2013) (Shift 2)

A system is described by the differential equation $\frac{d^{2}y\left(t\right)}{d{t}^2}+\frac{5dy\left(t\right)}{dt}+6y\left(t\right)=x\left(t\right)$. Let the x (t) be a rectangular pulse given by

x≤ft( t ) = ≤ft\{ {*20c 1 0 < t < 2\\ 0 otherwise } \}

Assuming that y(0) = 0 and $\frac{dy}{dt}=0$ at t = 0, the Laplace transform of y(t) is

A system described by a linear, constant co-efficient differential, ordinary, first order differential equation has an exact solution given by $y(t)$ for $t>0$, when the forcing function is $x(t)$ and initial condition is $y(0)$. If one wishes, to modify system so that the solution becomes $-2y(t)$ for $t>0$ we need to

Consider two identically distributed zero-mean random variable U and V. Let the cumulative distribution function of U and 2V be F(x) and G(x) respectively. Then, for all values of x.

The DFT of a vector [a b c d] is the vector [α, β, γ, δ]. Consider the product

[p q r s] = [a b c d]$\left[\begin{array}{cccc}a& b& c& d\\ d& a& b& c\\ c& d& a& b\\ b& c& d& c\end{array}\right]$. The DFT of the vector [ ] is a scaled version of

The signal flow graph for a system is given below.



The transfer function $\frac{Y\left(s\right)}{U\left(s\right)}$ for this system is