Simple Inverse Laplace Transform.

[jegues]

Homework Statement

Find the inverse Laplace Trasnform of,

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

Homework Equations

The Attempt at a Solution

We are given a table with a bunch of common Laplace transforms and their inverses but I can't seem to get this one.

Can anyone nudge me in the right direction or what I should start with?

Thanks again

 

[vela]

You could try partial fractions to break it up into less simplified pieces.

Do you know how to find inverse transforms using complex integrals?

 

[jegues]

You could try partial fractions to break it up into less simplified pieces.

Do you know how to find inverse transforms using complex integrals?

I don't think we've learned that yet, we just finished learning about the shifting theorem today.

 

[vela]

Try look at it this way:

$$F(s) = s\left[\frac{s}{(s^2+9)^2}\right] = sH(s)$$

Find h(t), the inverse Laplace transform of H(s)=s/(s²+9)². Then your table should show how f(t) and h(t) are related.

 

[jegues]

Try look at it this way:

$$F(s) = s\left[\frac{s}{(s^2+9)^2}\right] = sH(s)$$

Find h(t), the inverse Laplace transform of H(s)=s/(s²+9)². Then your table should show how f(t) and h(t) are related.

I can see that H(s) will transform to become cos3t but I'm not sure how to relate f(t) and h(t).

 

[vela]

No, the transform of cos 3t is s/(s²+9). It's similar but not quite the same as H(s).

Look into the properties of Laplace transforms regarding differentiation, both in the s domain and the time domain.