Laplace transform of an ODE with a non-smooth forcing function

  • #1

Homework Statement:

How do I deal with non-smooth forcing functions if I want to solve the Laplace transform of an ode.

Relevant Equations:

See below
Suppose I'm solving
$$y''(t) = x''(t)$$ where $$x(t)$$ is the ramp function. Then, by taking the Laplace transform of both sides, I need to know $x'(0)$ which is discontinuous. What is the appropriate technique to use here?
 

Answers and Replies

  • #2
STEMucator
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Check the screenshot I attached:



Screen Shot 2020-06-21 at 7.33.38 AM.png
 
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  • #3
jasonRF
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How is your course defining the Laplace transform? There is more than one way, especially with regards to how you treat the origin and singularities/discontinuities at the origin such as the one you are dealing with. By the way, the right-hand side of your problem is a delta functino: ##x^{\prime\prime}(t) = \delta(t)##.

Jason
 
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