Laplace Transform Practice: Finding Inverse and Basic Forms

[leopard]

Homework Statement

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.

 

[rootX]

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

 

[gabbagabbahey]

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

 

[NoMoreExams]

Homework Statement

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.

This is the best table I found if you need a quick answer in your research or to check your answer: http://www.vibrationdata.com/Laplace.htm.

For example check out 2.18, 2.20, and 2.21

 

[leopard]

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

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

 

[gabbagabbahey]

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

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

 

[leopard]

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