# Laplace transform

1. Dec 14, 2008

### leopard

1. The problem statement, all variables and given/known data

Find the laplace transform of t sin(t) and t cos(t), and the inverse transform of $$\frac{1}{(1+s^2)^2}$$

2. The attempt at a solution

I found the two laplace forms:

$$\frac{2s}{(s^2+1)^2}$$

and

$$\frac{s^2-1}{(s^2+1)^2}$$

I guess I'm supposed to use the two laplace transforms to find the inverse of this one, but I don't know how to do that.

2. Dec 14, 2008

### rootX

You can try convolution... doesn't look hard. I partially solved it.

3. Dec 14, 2008

### gabbagabbahey

Hint: what is the Laplace transform of $\sin(t)$?

4. Dec 14, 2008

### NoMoreExams

For example check out 2.18, 2.20, and 2.21

5. Dec 14, 2008

### leopard

$$\frac{1}{s^2 + 1}$$

6. Dec 14, 2008

### gabbagabbahey

Right, and so what is $$\mathcal{L}[\sin(t)-t\cos(t)]$$?

7. Dec 14, 2008

### leopard

Lol, it's so easy when you know the answer. One must be evil to give such a problem for the exam.