Laplace transformation question

In summary, the conversation revolves around solving a problem involving x"+3x'+2x=u(t-1)+2(t-2)u(t-2), x(0)=1, x'(0)=-1 using Laplace Transforms. The professor did not cover this topic in class but mentioned it may be on the test. The website Paul's Online Math Notes has a good introduction to Laplace Transforms and there are lecture videos on Physics Forums that demonstrate how to use LTs to solve ODEs for different forcing functions. However, Physics Forums is not a tutoring service and any follow-up questions can be posted on the forum after studying the material.
  • #1
sfgoat
10
0
Trying to answer the question:
x"+3x'+2x=u(t-1)+2(t-2)u(t-2), x(0)=1, x'(0)=-1

My book has the answer but I need to see how to solve a problem like this. Professor didn't have time to cover this section but he said one of these might be on the test. Any help is greatly appreciated.
 
Physics news on Phys.org
  • #2
Paul's Online Math Notes has a pretty good introduction to Laplace Transforms (and so should the text used in your DE course):

http://tutorial.math.lamar.edu/Classes/DE/LaplaceIntro.aspx

There are some lecture videos here:

https://www.physicsforums.com/threads/ordinary-differential-equations.110274/

Check out Post #10 at the link above. There are 3 or 4 videos which show how to use LTs to solve ODEs for various forcing functions.

Unfortunately, PF is not set up to be a tutoring service, so after studying the material, if you have any questions, please feel free to post any follow ups.
 

1. What is a Laplace transformation?

A Laplace transformation is a mathematical tool used to convert a function from the time domain to the frequency domain. It is often used in engineering and physics to solve differential equations and analyze systems.

2. How is a Laplace transformation performed?

A Laplace transformation involves taking the integral of a function multiplied by an exponential function. The result is a new function in the frequency domain, which can then be used to analyze the original function in the time domain.

3. What is the significance of Laplace transformation in science and engineering?

Laplace transformation is a powerful mathematical tool that allows scientists and engineers to solve complex differential equations and analyze systems in the frequency domain. It is used in a wide range of fields, including electrical and mechanical engineering, physics, and control systems.

4. Can Laplace transformation be used to solve real-world problems?

Yes, Laplace transformation is commonly used to solve real-world problems in various fields such as circuit analysis, control systems, and signal processing. It is a useful tool for finding solutions to differential equations that describe physical systems.

5. Are there any limitations to Laplace transformation?

While Laplace transformation is a powerful tool, it does have some limitations. It can only be used for linear systems and cannot handle discontinuous functions or functions with infinite discontinuities. Additionally, it may be challenging to apply in some cases due to the complexity of the integrals involved.

Similar threads

Laplace transform of cosine squared function
    • Calculus and Beyond Homework Help
Replies
1
Views
64
What is the Inverse Laplace Transform of e^(-sx^2/2)?
    • Calculus and Beyond Homework Help
Replies
10
Views
1K
Solving ##y'' - 5 y' - 6y = e^{3x}## using Laplace Transform
    • Calculus and Beyond Homework Help
Replies
7
Views
789
Laplace transform of ##f(t)=(u(t)-u(t-2\pi))\sin{t}##
    • Calculus and Beyond Homework Help
Replies
1
Views
89
Mellin transform of Dirac delta function ##\delta(t-a)##
    • Calculus and Beyond Homework Help
Replies
3
Views
2K
Laplace transform of an ODE with a non-smooth forcing function
    • Calculus and Beyond Homework Help
Replies
2
Views
1K
Does the Laplace Transform of e^(at)/t Exist?
    • Calculus and Beyond Homework Help
Replies
4
Views
1K
Determine limits of integration in double integral change of variables
    • Calculus and Beyond Homework Help
Replies
2
Views
160
Partial fraction decomposition with Laplace transformation in ODE
    • Calculus and Beyond Homework Help
Replies
9
Views
1K
Check on proof for property of the Laplace transform
    • Calculus and Beyond Homework Help
Replies
1
Views
625

Hot Threads

Recent Insights

Back
Top