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Find the inverse Laplace transform?

  1. Aug 8, 2013 #1
    1. The problem statement, all variables and given/known data
    Find the inverse Laplace transform of F(s)=(8s^2-4s+12)/(s(s^2+4)).


    2. Relevant equations
    A/s+(Bs+C)/(s^2+4)
    8s^2-4s+12=A(s^2+4)+(Bs+C)(s)=As^2+4A+Bs^2+Cs=s^2(A+B)+Cs+4A
    8=A+B
    C=-4
    A=3
    B=5
    L^-1 (3/s)+L^-1 ((5s-4)/(s^2+4))
    =3+ (Now I'm stucked.)



    3. The attempt at a solution
    The answer is f(t)=3-2 sin 2t+5 cos 2t.
     
  2. jcsd
  3. Aug 8, 2013 #2

    pasmith

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    Homework Helper

    [tex]
    \frac{5s - 4}{s^2 + 4} = 5\frac{s}{s^2 + 4} - 2\frac{2}{s^2 + 4}
    [/tex]

    Hopefully you should recognise the two terms on the right hand side as being Laplace transforms.
     
  4. Aug 9, 2013 #3
    Yes, I did. Thank you.
     
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