# Avoid problem with solving the LaplaceTransform and inversing it?

GROUPS:
 Hello all,I have been working on a project involving the Laplace equation. Sadly enough, somehow I don't get it to work. I have tried looking for a solution in the manual of Mathematica and tried several solutions, but non of them seem to work. Every time I end up getting the same thing, with the words LaplaceTransform and InverseLaplaceTransform, as I put in. I have tried using different domains for the NSolve, as well as reformulating the whole function which needs to be solved and trying different ways of formulating the variable t in the NSolve. The idea is that I get the Laplace transformation of the function (2nd line in the code), get a solution for variable t. After which the inverse Laplace transformation should be taking from this solution. My starting code is as following: Clear["Global*"] Sin[\[Omega] t] == q''[t]/Subscript[dw, 0]^2 + (2 \[Xi]q'[t])/Subscript[dw, 0] + q[t]/d LaplaceTransform[%, t, s] NSolve[%, t] InverseLaplaceTransform[%, s, t] Gratitude in advance.Kind regards, Justin Warners
Answer
10 months ago
3 Replies
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Answer
10 months ago
 HelloYou made a syntax mistake.  Sin[\[Omega] t] == q''[t]/Subscript[dw, 0]^2 + (2 \[Xi]q'[t])/Subscript[dw, 0] + q[t]/d It should be:  Sin[\[Omega] t] == q''[t]/Subscript[dw, 0]^2 + (2 \[Xi] q'[t])/Subscript[dw, 0] + q[t]/d You forgot a backspace to add between $\xi$ and q'(t)NSolve is a numerical solver, can't solve a symbolically.  Clear["Global*"] eq = Sin[\[Omega] t] == q''[t]/Subscript[dw, 0]^2 + (2*\[Xi] *q'[t])/Subscript[dw, 0] + q[t]/d eq1 = LaplaceTransform[eq, t, s] /. q[0] -> 0 /. q'[0] -> 0 (* Initial conditions,you may delete it or change to: eq1 = LaplaceTransform[eq, t, s] *) sol = First@Solve[eq1, LaplaceTransform[q[t], t, s]] // Simplify q[t] = InverseLaplaceTransform[LaplaceTransform[q[t], t, s] /. sol, s, t] 
Answer
10 months ago
 First, I think, you have a typo. There should be a blank between [Xi] and q'[t]).Then as far as I know one should solve the transformed equation for the Laplacetransform and then apply the inverse transformation (if possible). I did that as outlined in the notebook attached Attachments:
Answer
10 months ago