Simplifying Node Voltage Method for Finding Vo in Laplace Applications

In summary, the speaker is working on the crct and has been asked to use the "node voltage method" to find Vo. They are asking for help with checking their equation and finding an easier numerical approach for an upcoming exam. They share their equation for Vo(s) and ask for anyone else's solution. They also mention struggling with the partial fraction decomposition of the equation.
  • #1
Disar
28
0
I am currently working on the crct. in the attachment. I have been asked to find the "node voltage method" (i.e.-KCL) to determine Vo. I want to check my equation and was hoping someone can help. Also, I am trying to prepare for an exam and would like maybe an easier way numerically to approach this seeing that calculators are going to be out of the question. I would hate to have to find the roots of a decimal quadratic equation or soemthing of that nature.

I have Vo(s) equal to:

7.88E-6
(s^2 +(2.63E-8)*s +2.1E4)

Does anyone else come up with this?

If anyone has any ideas on how to make this a little cleaner and how to consistently do that in general, feel free, please. Also, the partial fraction decomposition of this is proving to be a real bear.

Thanks for the help
 

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  • #2
*clears throat* BUMP!
 
  • #3
You might want to write out the problem since no one is able to see the question with your "attachment pending approval."
 

What is Laplace transformation and how is it used in science?

Laplace transformation is a mathematical tool used to convert a function or equation in the time domain to the frequency domain. It is commonly used in science to analyze and solve differential equations, making it a useful tool in fields such as physics, engineering, and biology.

What are some real-world applications of Laplace transformation?

Laplace transformation has many practical applications, including signal processing, control systems, and circuit analysis. It is also used in fields such as finance to model stock market fluctuations and in epidemiology to model disease outbreaks.

How does Laplace transformation help in solving differential equations?

Laplace transformation simplifies differential equations by converting them into algebraic equations that are easier to solve. This makes it a valuable tool in solving a wide range of differential equations that may be difficult or impossible to solve using traditional methods.

What are the advantages and limitations of Laplace transformation?

The advantages of Laplace transformation include its ability to solve complex differential equations, its applicability to a wide range of fields, and its usefulness in signal processing and control systems. However, it does have limitations, such as only being applicable to linear systems and requiring initial conditions to be known.

Are there any alternative methods to Laplace transformation for solving differential equations?

Yes, there are other methods for solving differential equations, such as Fourier transformation and Z-transform. However, Laplace transformation is often preferred due to its simplicity and versatility in solving a wide range of differential equations.

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