How to Solve Inverse Laplace Transform: Factor or Use Complex Methods?

In summary, the speaker discusses their experience with taking the inverse Laplace transform of a function. They mention that they could have taken an easier route by factoring the expression, but instead chose to do it the more complex way, resulting in a different answer. They received zero points on the exam for this problem, but believe they should have received partial credit for demonstrating knowledge of partial fraction decomposition.
  • #1
eurekameh
210
0
2i734o0.png

I have to take the inverse laplace transform of the above function. Now, I know that I can factor (s^2+5s+6) as (s+3)(s+2) and take the easy way out. However, I did it as above on a test, getting A = -1, B = -1, and C = 1. I then took the inverse laplace transform and got something involving cosh's and sinh's. Doing it the easy way would have gotten you just the exponential e. This problem on the exam was maybe 30+ points and I got 0 points for this problem because I did not realize to factor (s^2+5s+6) and did it the way more complicated way. Is my method justified and most importantly, right?
 
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  • #2
Your method looks alright (so far), but you don't get the values you stated for A, B & C. Zero marks out of 30 seems a bit harsh though, as you at least demonstrated that you know partial fraction decomposition can be used for this. I'd talk to your professor to see if you can't get some partial credit for that at least.
 

Related to How to Solve Inverse Laplace Transform: Factor or Use Complex Methods?

1. What is an inverse Laplace transform?

An inverse Laplace transform is a mathematical operation that takes a function in the frequency domain and converts it back to its original form in the time domain. It is the reverse of the Laplace transform, which converts a function from the time domain to the frequency domain.

2. Why is the inverse Laplace transform important?

The inverse Laplace transform is important because it allows us to solve differential equations in the time domain by transforming them into algebraic equations in the frequency domain. This makes it a powerful tool in engineering, physics, and other fields where differential equations are commonly used.

3. How is the inverse Laplace transform calculated?

The inverse Laplace transform is calculated using the formula 1/(2πi) ∫F(s)e^(st)ds, where F(s) is the function in the frequency domain, t is the variable in the time domain, and the integral is taken along a path in the complex plane. This formula can be solved using various techniques, such as partial fraction decomposition, contour integration, and the Bromwich integral.

4. What are some applications of the inverse Laplace transform?

The inverse Laplace transform has a wide range of applications in fields such as control systems, signal processing, and circuit analysis. It is used to solve differential equations, analyze the stability of systems, and design filters and other electronic components.

5. Are there any limitations to the inverse Laplace transform?

Yes, there are some limitations to the inverse Laplace transform. One limitation is that not all functions have an inverse Laplace transform. In addition, the inverse Laplace transform may not exist for functions with poles that lie on the imaginary axis or for functions that grow too quickly in the complex plane. In these cases, alternative methods, such as the generalized inverse Laplace transform, may be used.

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