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Laplace transform of sin(ωt – Φ)

  1. Aug 13, 2008 #1

    I'm doing some preparation work for an upcoming mathematics module at University and I'm going over some Laplace transform questions.

    Part of one question asks for the Laplace transform of sin(ωt – Φ) and after looking the transform up I've found the answer to be (ω)cos(Φ) + (s)sin(Φ) / (S^2 + ω^2).

    Can anyone please tell me how to get there, because after attempting to transform using the normal method of integrating the function multiplied by e^-st I keep on hitting incorrect anwers.

    Many thanks to anyone who can help me out with this - it's driving me crazy!

    - Craig.
  2. jcsd
  3. Aug 13, 2008 #2


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    Homework Helper

    You should derive the Laplace transforms of sin(wt) and cos(wt), then expand out sin(wt+a) in terms of sin/cos (wt) and then apply the Laplace transform linearly.
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