Laplace Transform Problem

[wcz]

I face a difficulty in solving the following question.

The laplace transform of a signal x(t) that is zero for t<0 is

X(s) = [ s^3 + 2s^2 + 3s + 2] / [ s^4 + 2s^3 + 2s^2 + 2s + 2 ]

determine the laplace transform of the following signal;

y(t) = [t-1][x(t-1)] + dx(t)/dt

Thanks in advanced.

 

[nitu]

Hi..
The solution is
Y(s)= -exp(-s)X'(s)+sX(s)...

where exp is the exponential function and X'(s) is the first derivatve of X(s)...

Hope this helps..

 

[wcz]

Thanks for your reply.
Then, how about the following question.

y(t) = tx(t-1)

With the same given X(s).
Thanks in advanced.

 

[the_jackal]

The answer should be:

Y(s) = exp(-s)X'(s)

 

[steve10]

Here is the right answer:
Since y(t)=tx(t-1)=(t-1)x(t-1)+x(t-1), then Ly[y]=L[(t-1)x(t-1)]+L[x(t-1)]
=-exp(-s)X'(s)+exp(-s)X(s).

 

[the_jackal]

In my answer there should have been a negative sign as well plus that extra term that steve10 has shown.