Laplacetransform an Integral!

• Oct 2nd 2011, 02:48 AM
Muffin
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 $\displaystyle f(t)=2\int_{0}^{t}sin(9u)f'(t-u)du+sin9t,t\geq 0$ for f(t)

3. The attempt at a solution

Laplacetransforming:

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

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

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! =)
• Oct 2nd 2011, 04:28 AM
mr fantastic
Re: Laplacetransform an Integral!
Quote:

Originally Posted by Muffin
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 $\displaystyle f(t)=2\int_{0}^{t}sin(9u)f'(t-u)du+sin9t,t\geq 0$ for f(t)

3. The attempt at a solution

Laplacetransforming:

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

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

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 $\displaystyle F(s) = \frac{9}{(s - 9)^2}$.
• Oct 2nd 2011, 04:37 AM
Muffin
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?
• Oct 2nd 2011, 01:21 PM
mr fantastic
Re: Laplacetransform an Integral!
Quote:

Originally Posted by Muffin
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?
• Oct 3rd 2011, 05:00 AM
Ackbeet
Re: Laplacetransform an Integral!
Quote:

Originally Posted by Muffin
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 $\displaystyle f(t)=2\int_{0}^{t}sin(9u)f'(t-u)du+sin9t,t\geq 0$ for f(t)

3. The attempt at a solution

Laplacetransforming:

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

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

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?
• Oct 3rd 2011, 12:46 PM
mr fantastic
Re: Laplacetransform an Integral!
Quote:

Originally Posted by Ackbeet
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).