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Math Help - Inverse Laplace Transformation

  1. #1
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    Inverse Laplace Transformation

    I have been trying to get my head around this question, but i just can't seem to do it.

    Find the Inverse Laplace transform for:

    1/s^2(s+1)^2

    My steps:
    Partial fractions

    1/s^2(s+1)^2 = A/s + B/s^2 + C/(s+1) + D/(s+1)^2

    Then cross multiplication and collection of like terms

    1 = (A+B)(s+1)^2 + C(s+1) +(C+D)s^2 + A(s)

    then created 4 equations by substituting the following s values: -1,0,1,2

    Then used simultaneous equation solver on my calculator to solve the 4 equations, the calculator shows up with math error.

    Where am i going wrong?
    Point me in the right direction please.
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  2. #2
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    Quote Originally Posted by Kbotz View Post
    I have been trying to get my head around this question, but i just can't seem to do it.

    Find the Inverse Laplace transform for:

    1/s^2(s+1)^2

    My steps:
    Partial fractions

    1/s^2(s+1)^2 = A/s + B/s^2 + C/(s+1) + D/(s+1)^2

    Then cross multiplication and collection of like terms

    1 = (A+B)(s+1)^2 + C(s+1) +(C+D)s^2 + A(s)

    then created 4 equations by substituting the following s values: -1,0,1,2

    Then used simultaneous equation solver on my calculator to solve the 4 equations, the calculator shows up with math error.

    Where am i going wrong?
    Point me in the right direction please.
    Your process is correct so your mistake(s) will be in the details (which you have not provided).
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  3. #3
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    Oh cool ok
    Umm, my 4 equations after the substitution of s = 0,-1,1,2 are:

    equation 1 when s = 0

    1 = A + B + C

    equation 2 when s = -1

    1= -A+C+D

    equation 3 when s = 1

    1 = 5A+4B+3C+D

    equation 4 when s =2
    1 = 11A + 9B+ 7C + 4D
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  4. #4
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    Quote Originally Posted by Kbotz View Post
    I have been trying to get my head around this question, but i just can't seem to do it.

    Find the Inverse Laplace transform for:

    1/s^2(s+1)^2

    My steps:
    Partial fractions

    1/s^2(s+1)^2 = A/s + B/s^2 + C/(s+1) + D/(s+1)^2

    Then cross multiplication and collection of like terms

    1 = (A+B)(s+1)^2 + C(s+1) +(C+D)s^2 + A(s)

    then created 4 equations by substituting the following s values: -1,0,1,2

    Then used simultaneous equation solver on my calculator to solve the 4 equations, the calculator shows up with math error.

    Where am i going wrong?
    Point me in the right direction please.
    Putting the right hand side over the common denominator of s^2 (s + 1)^2 and equating numerators on each side, you get:

    1 = s(s+1)^2A + (s+1)^2B + (s+1)s^2C + s^2D.

    s = 0: 1 = B

    s = -1: 1 = D

    s = 1: .....

    Substitute B = D = 1 to get an equation with A and C.

    s = 2: ....

    Substitute B = D = 1 to get an equation with A and C.

    Solve for A and C simultaneously.
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  5. #5
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    it worked!
    thank you!
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