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Consider the function $$g\left( t \right) = {e^{ - t}}\,\sin \left( {2\pi t} \right)u\left( t \right)$$ ,where $$u(t)$$ ...
GATE ECE 2015 Set 3
The unilateral Laplace transform of $$f(t)$$ is $${1 \over {{s^2} + s + 1}}$$. Which one of the following is the unilate...
GATE ECE 2014 Set 4
If $$x\left[ N \right] = {\left( {1/3} \right)^{\left| n \right|}} - {\left( {1/2} \right)^n}\,u\left[ n \right],$$ then...
GATE ECE 2012
The unilateral Laplace transform of $$f(t)$$ is $$\,{1 \over {{s^2} + s + 1}}.$$ The unilateral Laplace transform of $$... GATE ECE 2012 Given that$$F(s)$$is the one-sided Laplace transform of$$f(t),$$the Laplace transform of$$\int\limits_0^t {f\left( ...
GATE ECE 2009
Consider the function $$f(t)$$ having laplace transform $$F\left( s \right) = {{{\omega _0}} \over {{s^2} + \omega _0^2... GATE ECE 2006 In what range should$$Re(s)$$remain so that the laplace transform of the function$${e^{\left( {a + 2} \right)t + 5}}$... GATE ECE 2005 The laplace transform of $$i(t)$$ is given by $$I\left( s \right) = {2 \over {s\left( {1 + s} \right)}}$$ As $$t \to \i... GATE ECE 2003 If$$\,\,L\left\{ {f\left( t \right)} \right\} = F\left( s \right)$$then$$\,\,\,L\left\{ {f\left( {t - T} \right)} \ri... GATE ECE 1999 If $$\,\,\,L\,\,\left\{ {f\left( t \right)} \right\} = {w \over {{s^2} + {w^2}}}$$ then the value of $$\mathop {Lim}\li... GATE ECE 1998 The laplace transform of$${e^{\alpha t}}\,\cos \,\alpha \,t$$is equal to ____________. GATE ECE 1997 The inverse laplace transform of the function$${{s + 5} \over {\left( {s + 1} \right)\left( {s + 3} \right)}}$$is ____... GATE ECE 1996 If$$L\left\{ {f\left( t \right)} \right\} = {{2\left( {s + 1} \right)} \over {{s^2} + 2s + 5}}$$then$$f\left( {{0^ + ... GATE ECE 1995 ## Marks 2 More The bilateral Laplace transform of a function $$f\left( t \right) = \left\{ {\matrix{ 1 & {if\,\,a \le t \le b} \cr... GATE ECE 2015 Set 2 A system is described by the following differential equation, where$$u(t)$$is the input to the system and$$y(t)$$is ... GATE ECE 2014 Set 1 Consider the differential equation$${{{d^2}y\left( t \right)} \over {d{t^2}}} + 2{{dy\left( t \right)} \over {dt}} + y... GATE ECE 2012 The Dirac delta Function $$\delta \left( t \right)$$ is defined as GATE ECE 2005 If $$\,\,\,$$$\$L\left\{ {f\left( t \right)} \right\} = {{s + 2} \over {{s^2} + 1}},\,\,L\left\{ {g\left( t \right)} \r...
GATE ECE 2000

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