LaPlace Transform of Heavy Side Function Homework

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In summary, the problem is to find the LaPlace transform of a function that is defined differently depending on the value of t. The first part of the function is equal to 0 while t is less than 1, and the second part is a quadratic equation when t is greater than or equal to 1. The attempt at a solution involves rewriting the function as a product and using known LaPlace transform formulas, but the person is unsure how to proceed due to the raised power in the function. They mention the possibility of using formulas for L(tn) or L(t*f(t)), and make a light-hearted comment about the name of the person who discovered the formula, Heaviside.
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TG3
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Homework Statement
While t<1 , f(t) =0
While t>= 1, f(t) = t^2-2t+2
Find the LaPlace transform of the given function.
The attempt at a solution
The problem can be re-written as: u1(t)(t^2-2t+2)

If it helps, this in turn can be re-written as: u1(t)((t-1)^2+1). I'm not sure it does help though.

As for how to proceed from here, I'm in a fog. I know the LaPlace transform for something of the form uc(t) y(t-c), but have no idea what to do with this problem because of the raised power.
 
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  • #2
Don't you have the formula for L(tn)?

Or the formula for L(t*f(t)) in terms of L(f(t))?

Oh, and the guy's name was Heaviside. He likely wasn't heavy on one side. :smile:
 

1. What is a Laplace Transform?

A Laplace Transform is a mathematical tool used to convert a function from the time domain to the frequency domain. It allows us to analyze complex systems and solve differential equations more easily.

2. What is the Heaviside Function?

The Heaviside Function, also known as the Unit Step Function, is a function that has a value of 0 for negative inputs and a value of 1 for positive inputs. It is commonly used in engineering and physics to model systems that have a sudden change or "jump".

3. How do you calculate the Laplace Transform of a Heaviside Function?

The Laplace Transform of a Heaviside Function is calculated using the formula L{u(t-a)} = e^(-as)/s, where a is the shift of the function and s is the variable in the frequency domain.

4. What is the significance of using the Laplace Transform on a Heaviside Function?

By using the Laplace Transform on a Heaviside Function, we can easily solve differential equations involving the function. It also helps us to understand the behavior and characteristics of the system more clearly in the frequency domain.

5. How is the Laplace Transform of a Heaviside Function used in real-world applications?

The Laplace Transform of a Heaviside Function is used in many real-world applications, such as in electronics, control systems, and signal processing. It allows engineers and scientists to analyze and design complex systems and predict their behavior accurately.

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