How Do You Apply Time Shift Properties in Laplace Transforms?

[indignant]

Hi guys, needing a bit of help understanding laplace transformations.

Homework Statement

1. f(t) = (t-4)u(t-2)
2. g(t) = (2e^-4t)u(t-1)
3. h(t) = 5 cos(2t-1)u(t)

Homework Equations

Laplace transform table.

The Attempt at a Solution

So basically I am given the laplace transform table, which also includes the properties. No derivation of equations is required. I am having trouble interpreting the table and somehow using the information to solve the question.

So.
Question 1;
the Laplace transform property I am using from the table is 'time shift' which says: L[f(t-a)u(t-a)] = (e^-as)(F(s))

So my equation is in the form f(t) = (t-4)u(t-2)
I change this to (t-2)u(t-2) - 2u(t-2).

this becomes (e^-2s)(F(s)) - (2e^-2s)/s
But what exactly should F(s) be?
I think I should try and understand the first question first before moving on to the other questions.
Cheers.

 

[CEL]

Hi guys, needing a bit of help understanding laplace transformations.

Homework Statement

1. f(t) = (t-4)u(t-2)
2. g(t) = (2e^-4t)u(t-1)
3. h(t) = 5 cos(2t-1)u(t)

Homework Equations

Laplace transform table.

The Attempt at a Solution

So basically I am given the laplace transform table, which also includes the properties. No derivation of equations is required. I am having trouble interpreting the table and somehow using the information to solve the question.

So.
Question 1;
the Laplace transform property I am using from the table is 'time shift' which says: L[f(t-a)u(t-a)] = (e^-as)(F(s))

So my equation is in the form f(t) = (t-4)u(t-2)
I change this to (t-2)u(t-2) - 2u(t-2).

this becomes (e^-2s)(F(s)) - (2e^-2s)/s
But what exactly should F(s) be?
I think I should try and understand the first question first before moving on to the other questions.
Cheers.

In your work you made
f(t-2) = t-2
so, f(t) = t and F(s) is the Laplace transform of t. F(s) = 1/s^2.

 

[MisterX]

It is confusing to put F(s) as part of the expression for the transform of the right side of the equation given for problem 1, because F(s) would typically be used for the transform of f(t) on the left side. So let's call the one from the right side G(s).

So to use the property, the let the term (t-2)u(t-2) = g(t-a)u(t-a)

what should g(t) be?
G(s) should be the Laplace transform of g(t).

 

[indignant]

I think I understand q1 (although I don't seem to be able to apply the knowledge to q2). Thanks.

For question 2; g(t) = (2e^-4t)u(t-1)

I use the property '(e^at)f(t) = F(s-a)'

I change g(t) to 2(e^-4)(e^-4(t-1))u(t-1)

I will ignore '2(e^-4)' since it is a constant.
so (e^-4(t-1))u(t-1) = (e^at)f(t).
What do I do now?
Thanks

 

[indignant]

I think this forum should have a 'solved' tag. (glorified bump)