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Laplace transform of phase-shifted sinusoid

  1. Aug 29, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the laplace transform of [TEX]f(t)=sin(4t+\frac{\pi}{3})u(t)[/TEX].
    http://img822.imageshack.us/img822/6996/codecogseqna.gif [Broken]

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    2. Relevant equations
    Definition of laplace transform, and properties: http://en.wikipedia.org/wiki/Laplace_transform#Properties_and_theorems"

    3. The attempt at a solution
    I have a feeling that I need to use the time-shift property of the transform, but I need just a bit more direction on the strategy.
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Aug 29, 2010 #2
    Use trig summation identity to simplify:

    [tex] f(t) = \left[ sin(4t)cos(\frac{\pi}{3}) + cos(4t)sin(\frac{\pi}{3}) \right] u(t). [/tex]

    Can you finish from here?
  4. Aug 30, 2010 #3
    When your step function starts, at t=0 ?
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