1

GATE ME 1997

Subjective

+1

-0

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 $$x=0$$ using the laplace transform technique?

$${{{d^2}y} \over {d{x^2}}} - 4{{dy} \over {dx}} + 3y = 0$$ with $$y=3$$ and

$${{dy} \over {dx}} = 7$$ at $$x=0$$ using the laplace transform technique?

2

GATE ME 1994

Fill in the Blanks

+1

-0

If $$f(t)$$ is a finite and continuous Function for $$t \ge 0$$ the laplace transformation is given by

$$F = \int\limits_0^\infty {{e^{ - st}}\,\,f\left( t \right)dt,} $$ then for $$f(t)=cos$$ $$h$$ $$mt,$$ the laplace transformation is ___________.

$$F = \int\limits_0^\infty {{e^{ - st}}\,\,f\left( t \right)dt,} $$ then for $$f(t)=cos$$ $$h$$ $$mt,$$ the laplace transformation is ___________.

3

GATE ME 1993

Fill in the Blanks

+1

-0

The laplace transform of the periodic function $$f(t)$$ described by the curve below

$$i.e.\,\,f\left( t \right) = \left\{ {\matrix{ {\sin \,t,} & {if\left( {2n - 1} \right)\pi < t < 2n\pi \left( {n = 1,2,3,...} \right)} \cr 0 & {otherwise\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,} \cr } } \right.$$ is ___________.

$$i.e.\,\,f\left( t \right) = \left\{ {\matrix{ {\sin \,t,} & {if\left( {2n - 1} \right)\pi < t < 2n\pi \left( {n = 1,2,3,...} \right)} \cr 0 & {otherwise\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,} \cr } } \right.$$ is ___________.

Questions Asked from Transform Theory (Marks 1)

Number in Brackets after Paper Indicates No. of Questions

GATE ME Subjects

Engineering Mechanics

Machine Design

Strength of Materials

Heat Transfer

Production Engineering

Industrial Engineering

Turbo Machinery

Theory of Machines

Engineering Mathematics

Fluid Mechanics

Thermodynamics

General Aptitude