Diff Eq problem, Laplace Transform

[DF19]

Homework Statement

Find the Laplace Transform of the given function
H(t-1)t^2

I'm not sure how to add (t-1) to the t^2 term to solve the problem

Any help would be greatly appreciated.

 

[poopcaboose]

That notation makes no sense, are you trying to translate the function on the s-axis? If you are what is the original function.

 

[poopcaboose]

If the original function is e^t*t^2 the translation = F(s-1) and since f(t)=t^2 its transform is 2/s^3, therefore you substitute s-1 in for s and get 2/(s-1)^3. Unless you are doing an inverse translation on the t-axis.

 

[DF19]

My book states that it is a H(t) is a heavyside function and I'm suppose to use the proposition:

L{H(t-c)f(t-c)}(s)=e^(-cs)F(s)

 

[poopcaboose]

Oh a unit step therefore you must translate both H(t) and F(t). LH(t-1)=e^s and f(t)=t^2, L(t^2)=2/s^3, so the transform is 2e^s/s^3