A system is described by the differential equation {d^{2}y (t) }/{dt^{2}} + \frac{5dy (t) }{dt} + 6y (t) = x (t) . Let the x (t) be a rectangular pulse given by x(t)={\\begin{array}{ccc}1 & 0&lt\ t&lt\ 2 \ 0 & \\\\text{ otherwise }\\\\\end{array}} Assuming that y(0) = 0 and \frac{dy}{dt} = 0 at t = 0, the Laplace transform of y(t) is

Correct Answer is : 1−e−2ss(s+2)(s+3)

\frac{e^{−2s}}{s (s + 2) (s + 3) }

\frac{1−e^{−2s}}{s (s + 2) (s + 3) }

\frac{e^{−2s}}{ (s + 2) (s + 3) }

\frac{1−e^{−2s}}{ (s + 2) (s + 3) }

GATE Electronics and Communications (EC) 2013 Solved Paper

Question : 46 of 65

Marks: +1, -0

A system is described by the differential equation

\;{d^{2}y\;(t)\;}/{dt^{2}} + \;{5dy\;(t)\;}/{dt} + 6y (t) = x (t)

. Let the x (t) be a rectangular pulse given by

x(t)={\{\table 1 , 0< t< 2 ; 0 , \;\text " otherwise "\;\}}

Assuming that y(0) = 0 and

\;{dy}/{dt} = 0

at t = 0, the Laplace transform of y(t) is

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