Solve Laplace Transform: te^t*H(t-1)

[nobodyuknow]

Homework Statement

Laplace transform: te^t*H(t-1)

Homework Equations

L{te^t} = 1/(s-1)^2
L{H(t-1)} = e-s/s

The Attempt at a Solution

Using e^(at)f(t) -> F(s-a)
with..e^(1t)H(t-1)
We can get, e^(-1s-1)/(s-1) = e^(-s-1)/(s-1) [I think?]
Thus applying tf(t) -> -dF/ds
Derive[e^(-s-1)/(s-1)] w.r.t. s, you get:
-se^(-s-1)/(s-1)^2

Which is close, but, not exact.

I know the answer is se^s-1/(s-1)^2

But how do they come to that?
I don't think the order of my working would affect the final outcome.

All help appreciated

 

[vela]

You need to show some attempt at solving the problem on your own.

 

[Ray Vickson]

Homework Statement

Laplace transform: te^t*H(t-1)

Homework Equations

L{te^t} = 1/(s-1)^2
L{H(t-1)} = e-s/s

The Attempt at a Solution

I know the answer is se^s-1/(s-1)^2

But how do they come to that?

How do you combine the two individual laplace transforms to calculate the final?

No. L{H(t-1)} is not e-s/s = e-1; it is e^(-s)/s. You must learn to use parentheses when writing things in plain text.

If I were doing the problem I would not bother trying to combine LTs using some "rules"; I would just write out the actual integration and go on from there.

 

[nobodyuknow]

Thanks, that was a mistake sorry

So basically use the integration rule and integrate te^t and then apply the Heaviside function?
I'm sorry, I'm not too confident with the Integral method, but..

integral{te^t} = (t-1)e^(t-st)

I'm not sure how to work from there.

[Googling Heaviside Integration as of now]

 

[Ray Vickson]

Thanks, that was a mistake sorry

So basically use the integration rule and integrate te^t and then apply the Heaviside function?
I'm sorry, I'm not too confident with the Integral method, but..

integral{te^t} = (t-1)e^(t-st)

I'm not sure how to work from there.

[Googling Heaviside Integration as of now]

What do you mean by the "integral method"? What do you think the Laplace transform of f(t) actually IS? Go back and look at the basic definitions---it is, by definition, an integral of a certain type. All the so-called "rules" you want to use are just properties of integrals, applied to some special cases.

And no, you do NOT do the integral and then apply the Heaviside function; the Heaviside function is part of the definition of f(t) in this case, and comes before any integrations.

It is not at all clear to me that you really understand what you are doing; that is why I suggest you go right back to square one and start with basic definitions.