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Solve the following initial value problem (DiracDelta function)

  1. Apr 27, 2012 #1
    1. The problem statement, all variables and given/known data
    y'' +4y = 2 delta(t - pi/4)

    where y(0)=0 and y'(0)=0

    2. Relevant equations
    Laplace transform
    Inverse Laplace transform


    3. The attempt at a solution
    after applying laplace tranform
    Y(s)=2e^((-pi/4)*s) / s^(2)+4

    as the final answer i have
    y(t) = U(t-pi/4)*2sin(t-pi/4)

    I'm not very comfortable with these types of problems yet, is my answer correct?
     
  2. jcsd
  3. Apr 27, 2012 #2
    I get the forward transform as:
    [itex]s^2\tilde{y}(s) +4\tilde{y}(s) =2e^{-s\pi /4}[/itex]
    Then isolating i get the same as you. But you got something wrong, the product of two functions cant be inverse transformed generally. The result should be:
    [itex] -\text{Heaviside}(t-\pi/4)\cos(2t)[/itex]
     
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