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orangeincup
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Homework Statement
So I know 1/(s-a)=e^(a1), but why is say, 2/((s+4)^2) equal to 2xe^-4x? Do I just simply add an X if the numeration is a constant other than 1?
Like I said, evaluate the LT of the expression with the x's and report back with what you got.orangeincup said:2*e^(-4*x) is what I get, I don't know where the other x came from.
Well I mean I know it's because it's squared, I just don't see how my laplace transform formula is giving me that
Let's see you do the integration. How come you didn't include the leading x in the integration?orangeincup said:L(2x*e^(-4x)) = 2x* 1/(s-4)
A Laplace transform is a mathematical tool used to convert a function of time into a function of complex frequency. It is commonly used in engineering and physics to analyze systems and solve differential equations.
The purpose of using a Laplace transform is to simplify the analysis of a system by converting it into a different domain. This can make it easier to solve differential equations and understand the behavior of a system.
To perform a Laplace transform, you can use a table of Laplace transforms or the definition of the transform, which involves integration. The transformed function will be a function of complex frequency, denoted as F(s).
The inverse Laplace transform is the process of converting a function of complex frequency back into a function of time. It is denoted as f(t) and can be found using a table of inverse Laplace transforms or by using the inverse Laplace transform formula.
Laplace transforms have many applications in engineering and physics, such as in circuit analysis, control systems, signal processing, and heat transfer. They are also used in solving differential equations and in Fourier analysis.