I can't seem to find the ways to solve the inverse laplace transform of: \(\displaystyle \, \dfrac{s^2\, +\, 2}{s^2\, +\, 2s\, +\, 5}\)
I used completing square to make it become: \(\displaystyle \, \dfrac{s^2\, +\, 2}{(s\, +\, 1)^2\, +\, 4}\)
The inverse laplace transform of: \(\displaystyle \, \dfrac{2}{(s\, +\, 1)^2\, +\, 4}\)
is e-t sin2t.
I am struck with: \(\displaystyle \, \dfrac{s^2}{(s\, +\, 1)^2\, +\, 4}\)
I do not know what to do next.
The final answer is ?(t) -(e-t/2 )(4cos2t + sin2t). However, I don't understand what the Dirac delta function is for. Can you guys help me? Thanks in advance.
I used completing square to make it become: \(\displaystyle \, \dfrac{s^2\, +\, 2}{(s\, +\, 1)^2\, +\, 4}\)
The inverse laplace transform of: \(\displaystyle \, \dfrac{2}{(s\, +\, 1)^2\, +\, 4}\)
is e-t sin2t.
I am struck with: \(\displaystyle \, \dfrac{s^2}{(s\, +\, 1)^2\, +\, 4}\)
I do not know what to do next.
The final answer is ?(t) -(e-t/2 )(4cos2t + sin2t). However, I don't understand what the Dirac delta function is for. Can you guys help me? Thanks in advance.
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