# Laplace Transformation Convolution Integral

• bmb2009
In summary, the conversation is about finding the Laplace transformation of a given function. The final answer is y(t)=2e^-2t +te^-2t +∫(t-τ)e^-2(t-τ) g(τ) dτ, but there may be errors in the earlier steps. The question also mentions the use of Laplace transformation tables and the need to factor terms in the given function.

## Homework Statement

I need to find the laplace transformation of the following function (and it's ok to leave it expressed as an integral). After doing the initial steps and algebra I got

Y(s)= g(t)/(s+2)^2 + 7(1/(s+2)^2)+ 2(1/(s+2)^2)

the answer is y(t)=2e^-2t +te^-2t +∫(t-τ)e^-2(t-τ) g(τ) dτ

We are allowed to use laplace transformation tables but what I don't understand is how to factor the terms in the Y(s) equation into a form which correlates in the base transformations. Any help would be great. Thanks

bmb2009 said:

## Homework Statement

I need to find the laplace transformation of the following function (and it's ok to leave it expressed as an integral). After doing the initial steps and algebra I got

Y(s)= g(t)/(s+2)^2 + 7(1/(s+2)^2)+ 2(1/(s+2)^2)

the answer is y(t)=2e^-2t +te^-2t +∫(t-τ)e^-2(t-τ) g(τ) dτ

Why is there a ##t## variable in your expression for ##Y(s)##?

LCKurtz said:
Why is there a ##t## variable in your expression for ##Y(s)##?

My bad it's G(s) which is not explicitly defined

bmb2009 said:
Y(s)= g(t)/(s+2)^2 + 7(1/(s+2)^2)+ 2(1/(s+2)^2)
Is there some reason you didn't combine the last two terms into 9/(s+2)2?

the answer is y(t)=2e^-2t +te^-2t +∫(t-τ)e^-2(t-τ) g(τ) dτ
If this is the answer, you need to recheck your earlier work for errors.

## 1. What is Laplace transformation convolution integral?

Laplace transformation convolution integral is a mathematical operation used in the field of signal processing to find the output of a linear system given its input. It involves integrating the product of the input signal and the impulse response of the system over a certain range of time.

## 2. How is Laplace transformation convolution integral different from regular convolution?

Laplace transformation convolution integral differs from regular convolution in that it uses Laplace transforms instead of regular time-domain signals. This allows for easier and more efficient calculations, especially for complex systems with multiple inputs and outputs.

## 3. What are the applications of Laplace transformation convolution integral?

Laplace transformation convolution integral has various applications in engineering, physics, and mathematics. It is commonly used in the analysis and design of control systems, electrical circuits, and signal processing systems.

## 4. What is the significance of the inverse Laplace transform in Laplace transformation convolution integral?

The inverse Laplace transform is used to convert the product of the Laplace transforms of the input signal and the impulse response into the convolution integral. This is an essential step in the calculation of the output of a linear system using Laplace transformation convolution integral.

## 5. Are there any limitations to using Laplace transformation convolution integral?

One limitation of Laplace transformation convolution integral is that it can only be applied to linear systems. Additionally, it may not be suitable for systems with non-linear or time-varying components. In such cases, other techniques such as Fourier transforms may be more appropriate.