# Homework Help: Laplace transformation problem

1. Sep 8, 2010

### jamshaid

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

L{4u(t-ர)cos2t}

2. Relevant equations

I have used UNIT STEP FUNCTION but could not get the result

3. The attempt at a solution

2. Sep 8, 2010

### vela

Staff Emeritus

3. Sep 8, 2010

### jamshaid

L{4u(t-ர)cos2t
f(t) = cos2t
F(s) = s/ s^2+4
therefore

4s e^-ர(cosர + sinர)/s^2 +4 Ans
________________________________
that is my work

4. Sep 8, 2010

### gabbagabbahey

Where is the factor the of $4e^{-\tau}(\sin\tau+\cos\tau)$ coming from? What rule are you trying to apply here?

5. Sep 9, 2010

### jamshaid

here is my solve, if I have done correctly.

6. Sep 10, 2010

### jamshaid

7. Sep 10, 2010

### vela

Staff Emeritus

8. Sep 10, 2010

### gabbagabbahey

It looks good to me (although you have a very strange way of writing $\pi$). On a side note, since trig functions are $2\pi$ periodic, you should have immediately recognized that $\cos(2t+2\pi)=\cos(2t)$ without appealing to a trig identity.

9. Sep 10, 2010

### vela

Staff Emeritus
I think the exponential term in the front incorrectly has an a in it rather than s.

10. Sep 10, 2010

### jamshaid

4e^(-as) s/(s^(2) + 4)

what do you think.........

11. Sep 11, 2010

### vela

Staff Emeritus
The variable a shouldn't be in the final answer.

12. Sep 14, 2010

### jamshaid

can you giving me some hints?