Finding the Laplace Transform of a Piecewise Function

In summary, a Laplace Transform is a mathematical tool used in engineering and physics to convert functions of time into functions of frequency. It is calculated by taking the integral of a function of time multiplied by e^-st. This technique has various applications, such as solving differential equations and analyzing circuits and control systems. It differs from Fourier Transform in its ability to handle more types of functions. The inverse Laplace Transform is the reverse process, converting functions in the frequency domain back to the time domain and is useful for solving differential equations.
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njnear
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Homework Statement



Find the Laplace Transform of:

f(t) = {0, t < 5
t2 - 10t + 31, t[tex]\geq5[/tex]

Homework Equations


The Attempt at a Solution



The answer I got was:

F(s) = e-5s (2/s3 + 6/s)

Is this correct?
 
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Can anyone help?
 
  • #3
Yes. It's right. You didn't really NEED help, did you?
 
  • #4
I just wanted to make sure it was correct. My book wasn't very clear on how to do the problem, so I wasn't sure. Thanks for confirming my answer. I really appreciate it.
 

What is a Laplace Transform?

A Laplace Transform is a mathematical tool used to solve problems in engineering and physics. It converts a function of time into a function of frequency, allowing for easier analysis of systems and signals.

How is a Laplace Transform calculated?

A Laplace Transform is calculated by taking the integral of a given function of time multiplied by the exponential function e^-st. The result is a new function in the frequency domain.

What are the applications of Laplace Transform?

Laplace Transform has many applications, including solving differential equations, analyzing the behavior of circuits, and studying the stability of control systems.

What is the difference between Laplace Transform and Fourier Transform?

The Laplace Transform and Fourier Transform are both techniques used to analyze functions in the time and frequency domains. However, the Laplace Transform is more versatile and can handle more types of functions, including those with discontinuities.

What is the inverse Laplace Transform?

The inverse Laplace Transform is the process of converting a function in the frequency domain back into the time domain. It is the reverse of the Laplace Transform and is useful for solving differential equations and recovering the original function.

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