GATE ME
Engineering Mathematics
Transform Theory
Previous Years Questions

## Marks 1

Laplace transform of the function $$f(t)$$ is given by $$f\left( s \right) = L\left\{ {f\left( t \right)} \right\} = \int\limits_0^\infty {f\left( t ... The Laplace transform of$${e^{i5t}}$$where$$i = \sqrt { - 1} ,$$Laplace transform of$$\cos \left( {\omega t} \right)$$is The Laplace Transform of$$f\left( t \right) = {e^{2t}}\sin \left( {5t} \right)\,u\left( t \right)$$is Laplace transform of$$\cos \,\left( {\omega t} \right)$$is$${s \over {{s^2} + {\omega ^2}.}}$$. The Laplace transform of$${e^{ - 2t}}\,\cos \left...
The function $$f(t)$$ satisfies the differential equation $${{{d^2}f} \over {d{t^2}}} + f = 0$$ and the auxiliary conditions, $$f\left( 0 \right) = 0,... The inverse Laplace transform of the function$$F\left( s \right) = {1 \over {s\left( {s + 1} \right)}}$$is given by The Laplace transform of$$f\left( t \right)$$is$${1 \over {{s^2}\left( {s + 1} \right)}}.$$The function The inverse Laplace transform of$${1 \over {\left( {{s^2} + s} \right)}}$$is If$$F(s)$$is the Laplace transform of the function$$f(t)$$then Laplace transform of$$\int\limits_0^t {f\left( x \right)dx} $$is Laplace transform of$${\left( {a + bt} \right)^2}$$where$$'a'$$and$$'b'$$are constants is given by: Solve the initial value problem$${{{d^2}y} \over {d{x^2}}} - 4{{dy} \over {dx}} + 3y = 0$$with$$y=3$$and$${{dy} \over {dx}} = 7$$at$$x=0$$us... If$$f(t)$$is a finite and continuous Function for$$t \ge 0$$the laplace transformation is given by$$F = \int\limits_0^\infty {{e^{ - st}}\,\,f\...
The laplace transform of the periodic function $$f(t)$$ described by the curve below i.e.\,\,f\left( t \right) = \left\{ {\matrix{ {\sin \,t,} &...
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