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Math Help - Laplacetransform an Integral!

  1. #1
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    Unhappy Laplacetransform an Integral!

    1. The problem statement, all variables and given/known data
    Hey! I have tried to solve this problem but I get stuck when it comes to the inverstransforming. Anyway here is the problem and my attempt to a solution:

    Solve f(t)=2\int_{0}^{t}sin(9u)f'(t-u)du+sin9t,t\geq 0 for f(t)

    3. The attempt at a solution

    Laplacetransforming:

    F(s)=\frac{18}{s^{2}+9^{2}}sF(s) + \frac{9}{s^{2}+9^{2}}

    Solving F(s)
    F(s)=\frac{9}{s^{2}+9^{2}-18s}

    I dont know what to do now, with the inverstransform? And the F(s) feels wrong..Is my Laplacetransforming correct? I have tried to use the convolution theorem..but I dont know if I used it correct..

    Thanks! =)
    Last edited by Muffin; October 2nd 2011 at 12:46 PM.
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  2. #2
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    Re: Laplacetransform an Integral!

    Quote Originally Posted by Muffin View Post
    1. The problem statement, all variables and given/known data
    Hey! I have tried to solve this problem but I get stuck when it comes to the inverstransforming. Anyway here is the problem and my attempt to a solution:

    Solve f(t)=2\int_{0}^{t}sin(9u)f'(t-u)du+sin9t,t\geq 0 for f(t)

    3. The attempt at a solution

    Laplacetransforming:

    F(s)=\frac{18}{s^{2}+9^{2}}sF(s) + \frac{9}{s^{2}+9^{2}}

    Solving F(s)
    F(s)=\frac{9}{s^{2}+9^{2}-18s}

    I dont know what to do now, with the inverstransform? And the F(s) feels wrong..Is my Laplacetransforming correct? I have tried to use the convolution theorem..but I dont know if I used it correct..

    Thanks! =)
    Assuming that your calculations are correct you should note that F(s) = \frac{9}{(s - 9)^2}.
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  3. #3
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    Re: Laplacetransform an Integral!

    Okey thx, But its still something wrong bcs in the end it should be f(t)= sin9t.

    And this answer will give me that f(t)= 9te^(9t).

    Do you know what am I doing wrong?
    Last edited by Muffin; October 2nd 2011 at 12:37 PM.
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  4. #4
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    Re: Laplacetransform an Integral!

    Quote Originally Posted by Muffin View Post
    Okey thx, But its still something wrong bcs in the end it should be f(t)= sin9t.

    And this answer will give me that f(t)= 9te^(9t).

    Do you know what am I doing wrong?
    It should be clear that f(t)= sin(9t) does not solve the integral equation you posted. Did you test it?
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  5. #5
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    Re: Laplacetransform an Integral!

    Quote Originally Posted by Muffin View Post
    1. The problem statement, all variables and given/known data
    Hey! I have tried to solve this problem but I get stuck when it comes to the inverstransforming. Anyway here is the problem and my attempt to a solution:

    Solve f(t)=2\int_{0}^{t}sin(9u)f'(t-u)du+sin9t,t\geq 0 for f(t)

    3. The attempt at a solution

    Laplacetransforming:

    F(s)=\frac{18}{s^{2}+9^{2}}sF(s) + \frac{9}{s^{2}+9^{2}}

    Solving F(s)
    F(s)=\frac{9}{s^{2}+9^{2}-18s}

    I dont know what to do now, with the inverstransform? And the F(s) feels wrong..Is my Laplacetransforming correct? I have tried to use the convolution theorem..but I dont know if I used it correct..

    Thanks! =)
    Do you happen to know that f(0) = 0?
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  6. #6
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    Re: Laplacetransform an Integral!

    Quote Originally Posted by Ackbeet View Post
    Do you happen to know that f(0) = 0?
    From what I can see, the OP used f(0) = 0 (but whether by default or knowledge, I can't tell).
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