Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

masroorm

  • 3 years ago

Does anyone know how to find the Inverse Laplace Transform of 6/(s^3+3s)

  • This Question is Open
  1. athe
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    It is combination of simple Laplace transformation:\[\frac{6}{s^3+3s}=\frac{6}{s(s^2+3)}\] Use Method of undetermined coefficients: \[\frac{6}{s(s^2+3)} \rightarrow \frac{2}{s}-\frac{2s}{s^2+3}\] Use well know transformation for this functions: \[\frac{2}{s} \rightarrow 2\cdot H(t)\], H(t) - Heaviside step function \[\frac{2s}{s^2+3}\rightarrow 2\cdot \cos(\sqrt{3}t)\] \[\frac{6}{s^3+3s} \rightarrow 2\cdot H(t) +2\cdot \cos(\sqrt{3}t)\]

  2. honey26
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    we know that L[sin 3^(1/2) t]= (3^(1/2))/(s^2+3) and L[integral f(k) dk (in limits 0 to t)]=L[f(t)]/s. Here we can consider f(t)=sin 3^(1/2) t,then (3^(1/2))/s(s^2 +3) =integral f(k) dk in limits 0 to t .the integral value is 1-(cos3^(1/2) t)/(3^(1/2)). therefore, L[6/((s^3)+3s)] = 2(1-(cos3^(1/2) t)/(3^(1/2)).

  3. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy