# Step Function (heaviside) laplace xform

• chota
In summary, the conversation discusses finding the Laplace transform of a given function, specifically f(t) = (t-2)^2 * u(t-2). The person is unsure if they have the correct function and is seeking help with solving it. The solution involves using a translation property of the Laplace transform and integrating by parts.
chota
Hi, I currently have this problem to solve and I can't seem to figure it out

it goes like this

Find the Laplace transform of the given function:

f(t) = { 0 t<2, (t-2)^2 t>=2

I tried working it out and this is where i get stuck

f(t) = (t-2)^2 * u(t-2)

I am not sure if I got the write function for f(t), but if I did, I am not sure how to go on with solving this.
Any help is appreciated, Thank YOu
Chota

Did you consider integrating it directly?
The laplace transform of function f(t) is defined as
$$\int_0^\infty e^{-st}f(t)dt[/itex] and here [tex]\int_0^\infty e^{-st}(t-2)^2 u(t-2)dt= \int_2^\infty (t-2)^2e^{-st}dt$$

and that can be integrated using integration by parts, twice.

chota said:
Hi, I currently have this problem to solve and I can't seem to figure it out

it goes like this

Find the Laplace transform of the given function:

f(t) = { 0 t<2, (t-2)^2 t>=2

I tried working it out and this is where i get stuck

f(t) = (t-2)^2 * u(t-2)

I am not sure if I got the write function for f(t), but if I did, I am not sure how to go on with solving this.
Any help is appreciated, Thank YOu
Chota

You need to make use of a translation property of the Laplace transform. It states that:
if F(s) is the Laplacetransform of f(t) then L{f(t-a)u(t-a)}=exp(-as)F(s)

Can you apply this to your problem?

## What is a step function?

A step function, also known as a Heaviside function, is a mathematical function that returns a constant value for all values of its input variable greater than or equal to a specified value, and returns zero for all other values.

## What is the Laplace transform of a step function?

The Laplace transform of a step function is a mathematical operation that transforms a function from the time domain to the frequency domain. Specifically, the Laplace transform of a step function is equal to 1/s, where s is the complex frequency variable.

## What is the significance of the step function in mathematics?

The step function is commonly used in mathematics to model real-world phenomena that have sudden changes at specific points, such as in electrical circuits or control systems. It is also used in signal processing to filter out unwanted frequencies.

## What are the properties of the step function?

The step function has two main properties: the value of the function is equal to 0 for all negative inputs, and the value of the function is equal to 1 for all non-negative inputs. It is also a discontinuous function, meaning it has jump discontinuities at the specified value.

## How is the Laplace transform of a step function calculated?

The Laplace transform of a step function can be calculated using the formula 1/s, where s is the complex frequency variable. This formula can be derived from the definition of the Laplace transform and the properties of the step function.

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