Laplace domain to time domain

In summary, the question is about finding the maximum of a three exponential equation using Laplace transforms. The first derivative of the equation is taken and equated to zero, resulting in a three exponential equation for f'(t). After taking the Laplace transform for f'(t), a third degree equation in "s" is obtained. By solving the cubic equation, three values of "s" are found. The remaining task is to find "t" at which f(t) is max and convert "s=some constant" to "t".
  • #1
abhishek.akku
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Homework Statement



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??



Homework Equations





The Attempt at a Solution

 
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  • #2
I have taken the Laplace transform of f'(t) and obtained a cubic equation in "s". I solved the cubic equation for s and got 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" ?
 

1. What is the Laplace domain?

The Laplace domain is a mathematical representation of a function in the complex frequency domain. It is used to analyze and solve differential equations.

2. What is the time domain?

The time domain is a mathematical representation of a function in the time dimension. It is used to analyze and understand the behavior of a system over time.

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

To convert from Laplace domain to time domain, you need to use the inverse Laplace transform. This involves manipulating the function in the complex frequency domain to solve for the original function in the time domain.

4. What is the purpose of converting from Laplace domain to time domain?

Converting from Laplace domain to time domain allows us to understand the behavior of a system in the time dimension. It is particularly useful in analyzing systems with complex dynamics, such as electrical circuits or control systems.

5. Can you give an example of converting from Laplace domain to time domain?

Sure, let's say we have a transfer function in the Laplace domain, such as H(s) = 1/(s+2). To convert this to the time domain, we use the inverse Laplace transform and solve for the function h(t). In this case, h(t) = e^(-2t).

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