A system is described by the differential equation $${{{d^2}y} \over {d{t^2}}} + 5{{dy} \over {dt}} + 6y\left( t \right) = x\left( t \right).$$ Let x(t) be a rectangular pulse given by
$$x\left( t \right) = \left\{ {\matrix{
{1,} & {0 < t < 2} \cr
{0,} & {{\rm{otherwise}}} \cr
} } \right.$$
Assuming that y(0) = 0 and $${{dy} \over {dt}} = 0$$ at t = 0, the Laplace transform of y(t) is
A. $${{{e^{ - 2s}}} \over {s\left( {s + 2} \right)\left( {s + 3} \right)}}$$
B. $${{1 - {e^{ - 2s}}} \over {s\left( {s + 2} \right)\left( {s + 3} \right)}}$$
C. $${{{e^{ - 2s}}} \over {\left( {s + 2} \right)\left( {s + 3} \right)}}$$
D. $${{1 - {e^{ - 2s}}} \over {\left( {s + 2} \right)\left( {s + 3} \right)}}$$
Answer: Option B
This Question Belongs to Electronics And Communications Engineering >> Signal Processing
The Fourier transform of a real valued time signal has
A. Odd symmetry
B. Even symmetry
C. Conjugate symmetry
D. No symmetry
A. $$V$$
B. $${{{T_1} - {T_2}} \over T}V$$
C. $${V \over {\sqrt 2 }}$$
D. $${{{T_1}} \over {{T_2}}}V$$
A. $$T = \sqrt 2 {T_s}$$
B. T = 1.2Ts
C. Always
D. Never
A. $${{\alpha - \beta } \over {\alpha + \beta }}$$
B. $${{\alpha \beta } \over {\alpha + \beta }}$$
C. α
D. β
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