How to find this laplace transformation?

In summary, to determine the Laplace transformation of a given function, one can use the Laplace transform table and apply its properties to simplify the expression. Laplace transformation is commonly used in scientific research to solve differential equations and make them more manageable. Some common mistakes to avoid when finding Laplace transformations include not properly defining the time and frequency domains and not correctly applying the properties of the transform. To ensure correctness, one can check their answer by taking the inverse Laplace transform. Although there are alternative methods, using the Laplace transform table and properties is the most efficient approach.
  • #1
kloong
36
0
System: U(s) ---> H(s) ----> Y(s)

the transfer fuction is: H(s) = s^2 / ( (s+1)(s^2 + 2s + 2) )

how to find the lapalace transform Y(s) of the output when the input is a unit step function?then how about the output time response y(t) (without imaginary terms) when the input is a unit step fuction?

thanks.
 
Last edited:
Physics news on Phys.org
  • #2
You know that the transfer function is given by [itex]H(s)=Y(s)/U(s)[/itex]. What is the Laplace transform of the unit step function?
 

1. How do I determine the Laplace transformation of a given function?

In order to find the Laplace transformation of a function, you can use the Laplace transform table to identify the corresponding transformation for each term in the function. Then, you can apply the properties of the Laplace transform to simplify the expression and find the final transformation.

2. What is the purpose of using Laplace transformation in scientific research?

Laplace transformation is commonly used in scientific research to simplify and solve differential equations, which are often used to describe physical phenomena. It allows for easier manipulation and analysis of these equations, making them more manageable to solve.

3. Are there any common mistakes to avoid when finding Laplace transformations?

One common mistake is forgetting to properly define the time domain and frequency domain of the function. It is important to pay attention to the notation and make sure to use the correct variables in the transformation process. Another mistake is not properly applying the properties of the Laplace transform, which can lead to incorrect results.

4. How do I know if I have correctly found the Laplace transformation?

You can check your answer by taking the inverse Laplace transform of the resulting transformation. If you get back the original function, then you have correctly found the Laplace transformation.

5. Are there any alternative methods for finding Laplace transformations?

Yes, there are alternative methods such as using partial fraction decomposition or using convolution with the unit step function. However, the Laplace transform table and properties are the most commonly used and efficient methods for finding Laplace transformations.

Similar threads

Solving ##y'' - 5 y' - 6y = e^{3x}## using Laplace Transform
    • Calculus and Beyond Homework Help
Replies
7
Views
788
What is the Inverse Laplace Transform of e^(-sx^2/2)?
    • Calculus and Beyond Homework Help
Replies
10
Views
1K
Does the Laplace Transform of e^(at)/t Exist?
    • Calculus and Beyond Homework Help
Replies
4
Views
1K
Solving an ODE with the Laplace transform
    • Calculus and Beyond Homework Help
Replies
8
Views
2K
Partial fraction decomposition with Laplace transformation in ODE
    • Calculus and Beyond Homework Help
Replies
9
Views
1K
Mellin transform of Dirac delta function ##\delta(t-a)##
    • Calculus and Beyond Homework Help
Replies
3
Views
2K
Laplace transform of the multiplication of two functions
    • Calculus and Beyond Homework Help
Replies
4
Views
2K
Finding the Laplace transform of a piecewise function
    • Calculus and Beyond Homework Help
Replies
3
Views
799
Laplace transform applied to a differential equation
    • Calculus and Beyond Homework Help
Replies
1
Views
672
A tricky inverse Laplace transform
    • Calculus and Beyond Homework Help
Replies
8
Views
2K

Hot Threads

Recent Insights

Back
Top