Laplace domain to time domain

In summary, the conversation discusses the process of finding the maximum value of a three-exponential equation using Laplace transforms. The speaker has taken the first derivative and equated it to zero, resulting in a third-degree equation in "s". They then solved for "s" and need help converting it back to "t" using the inverse Laplace transform and the residue theorem.
  • #1
abhishek.akku
2
0
i have a question about laplace transforms. I had to find the maximum of a three exponential equation f(t). What I have done is took the first derivative of f(t) and equated it to zero. Now f'(t) is also a three exponential equation ( like f'(t)= e^at +e^bt +e^ct). So I have taken laplace transform for f'(t) = sf(s)-f(0) and obtained a 3rd digree equation in "s". I have solved the cubic equation for f(s) and found out three values of s. Now I need to find out "t" at which f(t) is max.

How can I convert "s= some constant" to "t" ? Can anybody help me out??
 
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  • #2
The equation that you have obtained with the Laplace transform is a polynomial equation in "s". To convert this back to "t", you need to use the inverse Laplace transform. The inverse Laplace transform of a polynomial equation is can be obtained using the residue theorem.
 

1. What is the Laplace domain?

The Laplace domain is a mathematical technique used to analyze systems and signals in the frequency domain. It utilizes the Laplace transform, which converts a function of time into a function of complex frequency. This allows for the analysis of signals and systems with complex behavior.

2. What is the time domain?

The time domain is a method of analyzing systems and signals based on their behavior over time. It is the most intuitive domain and represents the changes of a signal or system over time.

3. How do you convert from Laplace domain to time domain?

To convert from Laplace domain to time domain, you must use the inverse Laplace transform. This involves applying a mathematical formula to the function in the Laplace domain to transform it back into the time domain.

4. Why is it useful to convert from Laplace domain to time domain?

Converting from Laplace domain to time domain allows for a better understanding of the behavior of a system or signal over time. It also allows for the application of techniques such as differential equations and system analysis to further analyze and manipulate the signal.

5. Can any signal or system be converted from Laplace domain to time domain?

Yes, any signal or system that can be represented by a function of time can be converted from Laplace domain to time domain. However, if the function is not well-behaved or does not have a Laplace transform, the conversion may not be possible or may produce unreliable results.

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