LAPLACE TRANSFORMATION1. INTRODUCTION

2. PROPERTIES OF LAPLACE

3. INERSE OF LAPLACE TRANSFORMATION

4. PERIODIC FUNCTION

INTRODUCTION:Laplace transforms has been integral part of mathematical techniques used by engineers as well as scientists. The laplace transformation was named after mathematician and astronomer pierre-simon laplace. In recent years it use as mathematical tool for higher engineering have increase in leaps and bound. This is because the transform method provides a simple and effective means for the solution of many problem arising in engineering.

DEFINITION :Let f(t) be a function of t, defined for all positive values of t , then the laplace transform of f(t) denoted by L[f(t)] and defined As provided the integral exists. Here s is

parameter which may real or complex.

  

SOME OF THE FORMULAS USED IN LAPLACE TRANSFORMATION:

we know that

Properties of laplace tranforms:

1. Linearity property:If a,b,c be any contants and f,g,h are some function of t

then

2. First Shifting Property:

Multiplication by power of ‘t’:

INVERSE OF LAPLACE TRANSFORMATION:

Inverse of laplace transformation is reverse process of laplace transformation . As we know integration is the reverse process of differentiation similarly inverse laplace transformation is reverse process of laplace transformation.

STANDARD LAPLACE FORMULAS TO INVERSE LAPLACE FORMULAS:

Sr No. Laplace transform Inverse transform

1

2

3

4

5

6

Solution:

PERIODIC FUNCTIONA function f(t) is said to be periodic function of

period T.If (t +T) = f(t) T>0 Eg,

is periodic function of period The laplace transform of periodic function defined is

1) Find laplace Transform

and .

is periodic function of Period Tthus laplace transform is given by

T

0

T

0T

0

T

T

0

0

0

T

0

0

0

0

T

T

T

T