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ritzmax72
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Please anyone tell me how laplace transformation is derived. It transform a funtion into new one. Then what we get? Any example to show how it make a function easy to solve?
paulfr said:A Fourier Transform converts a Steady State Time Domain function/signal to the Frequency Domain.
Basically it integrates [adds up] the energy at differenct frequecies to obtain the signal's spectrum.
It is what a Spectrum Analyzer does.
A variable frequency filter measures the energy at different frequencies
The Laplace Transform [LT] does the same thing but for Transient [non Steady State] signals and can
show the transient response. It is a fundamental tool in Dynamics as both signals and
"black boxes" have a LT and you can just multiply them to get the output response in the Complex Domain.
Then an Inverse Transform produces the output in the Time Domain.
Laplace Transformation is a mathematical technique used to convert a function of time into a function of complex frequency. It is commonly used in engineering and physics to solve differential equations and analyze dynamic systems.
The purpose of Laplace Transformation is to simplify the process of solving differential equations, which can be complex and time-consuming. It transforms the equation into an algebraic equation that can be easily manipulated and solved using standard mathematical techniques.
One of the main advantages of Laplace Transformation is that it allows for the solution of differential equations that cannot be solved using traditional methods. It also provides a general solution that can be used to solve a wide range of problems and can be easily applied to systems with multiple inputs and outputs.
While both Laplace Transformation and Fourier Transformation are used to convert functions of time into functions of frequency, they have different applications. Laplace Transformation is used to solve differential equations and analyze dynamic systems, while Fourier Transformation is used to decompose a function into its frequency components.
Laplace Transformation is used in various fields, including electrical engineering, mechanical engineering, and physics. It is commonly used in the design and analysis of control systems, circuits, and mechanical systems. It is also used in signal processing, image analysis, and fluid dynamics.