Transform Theory · Engineering Mathematics · GATE EE

The solution of the differential equation, for $$t > 0,\,\,y''\left( t \right) + 2y'\left( t \right) + y\left( t \right) = 0$$ with initial condit...

The Laplace transform of $$f\left( t \right) = 2\sqrt {t/\pi } $$$$\,\,\,\,\,$$ is$$\,\,\,\,\,$$ $${s^{ - 3/2}}.$$ The Laplace transform of $$g\left( ...

Let $$X\left( s \right) = {{3s + 5} \over {{s^2} + 10s + 20}}$$ be the Laplace Transform of a signal $$x(t).$$ Then $$\,x\left( {{0^ + }} \right)$$ i...

If $$x\left[ N \right] = {\left( {1/3} \right)^{\left| n \right|}} - {\left( {1/2} \right)^n}\,u\left[ n \right],$$ then the region of convergence $$(...

The unilateral Laplace transform of $$f(t)$$ is $$\,{1 \over {{s^2} + s + 1}}.$$ The unilateral Laplace transform of $$t$$ $$f(t)$$ is

Given $$f\left( t \right) = {L^{ - 1}}\left[ {{{3s + 1} \over {{s^3} + 4{s^2} + \left( {k - 3} \right)}}} \right].$$ $$\mathop {Lt}\limits_{t \to \p...

Let $$Y(s)$$ be the Laplace transform of function $$y(t),$$ then the final value of the function is __________.

The Laplace transform of $$\,\left( {{t^2} - 2t} \right)\,u\left( {t - 1} \right)$$ is ______________.

The Laplace transform of $$f(t)$$ is $$F(s).$$ Given $$F\left( s \right) = {\omega \over {{s^2} + {\omega ^2}}},$$ the final value of $$f(t)$$ is ___...

Consider the differential equation $${{{d^2}y\left( t \right)} \over {d{t^2}}} + 2{{dy\left( t \right)} \over {dt}} + y\left( t \right) = \delta \lef...

Given $$f(t)$$ and $$g(t)$$ as shown below $$g(t)$$ can be expressed as...

Given $$f(t)$$ and $$g(t)$$ as shown below The laplace transform of $$g(t)$$ is ...