Inverse Laplace : with Convolution

[masterchiefo]

Homework Statement

Use the convolution property to obtain the inverse Laplace transform of
F(s)= e^-3s * ((3s+15)/s²+25)

Homework Equations

The Attempt at a Solution

= (3*(s/s²+5²) + 15*(1/s²+5²)) *e^-3s

Using table of Laplace:
3*(s/s²+5²) = 3*cos(5*t) = T7
15*(1/s²+5²) = 15/5*sin(5*t) =T18
e^-3s = s(t-a) = s(t-3) (T16)

=(3*cos(5*t)+15/5*sin(5*t))*s(t-3)

Convolution : int 0 to t (f(u)*g(t-u))du
integral 0 to t ((3*cos(5*u)+15/5*sin(5*u))*s((t-u)-3)) du

Something is wrong in my work here, and I can't find where. :([/SUP]

 

[LCKurtz]

Homework Statement

Use the convolution property to obtain the inverse Laplace transform of
F(s)= e^-3s * ((3s+15)/s²+25)

Homework Equations

The Attempt at a Solution

= (3*(s/s²+5²) + 15*(1/s²+5²)) *e^-3s

Using table of Laplace:
3*(s/s²+5²) = 3*cos(5*t) = T7
15*(1/s²+5²) = 15/5*sin(5*t) =T18
e^-3s = s(t-a) = s(t-3) (T16)

None of the above equalities are true; you have functions of s "equal" to functions of t.

=(3*cos(5*t)+15/5*sin(5*t))*s(t-3)

Convolution : int 0 to t (f(u)*g(t-u))du
integral 0 to t ((3*cos(5*u)+15/5*sin(5*u))*s((t-u)-3)) du

Something is wrong in my work here, and I can't find where. :([/SUP]

And you are apparently using s for two different things. With 156 posts, it is past time for you to learn to use latex. It isn't worth the effort to decipher what you have written.

 

[vela]

Homework Statement

Use the convolution property to obtain the inverse Laplace transform of
F(s)= e^-3s * ((3s+15)/s²+25)

Is the asterisk supposed to denote multiplication or convolution?

You need to use parentheses as appropriate. Assuming the asterisk is supposed to be multiplication, what you wrote means
$$F(s) = e^{-3s}\left(\frac 3s + \frac{15}{s^2} + 25\right),$$ which is quite different from what you intended.

Using table of Laplace:
3*(s/s²+5²) = 3*cos(5*t) = T7
15*(1/s²+5²) = 15/5*sin(5*t) =T18
e^-3s = s(t-a) = s(t-3) (T16)

=(3*cos(5*t)+15/5*sin(5*t))*s(t-3)

Is there some reason you're not simplifying 15/5?

Convolution : int 0 to t (f(u)*g(t-u))du
integral 0 to t ((3*cos(5*u)+15/5*sin(5*u))*s((t-u)-3)) du

Something is wrong in my work here, and I can't find where. :([/SUP]

Why do you think something's wrong?

Besides the problems LCKurtz pointed out with what you've written, did you notice that when you wrote "=(3*cos(5*t)+15/5*sin(5*t))*s(t-3)," you never said what it was equal to and that you're using * to mean both multiplication and convolution? You should make an effort to be less sloppy, especially when you're trying to communicate with others.