Laplace Transform question with unit step function

[jamesdocherty]

Homework Statement

Homework Equations

Laplace Trasformations

The Attempt at a Solution

a. done
b. f(t)= t -3*t*u(t-1) + 4*u(t-1) -3*u(t-2) -2*t*(t-2)
c. 1/(s^2) - (3e^-s -2e^-2s)/(s^3) + (4e^-s -3e^-2s)/s
d. 1/(s-1) * (1/(s^2) - (3e^-s -2e^-2s)/(s^3) + (4e^-s -3e^-2s)/s)

These are the answers i got but my friend got all different ones and we are not sure who is correct. Thanks for any help.

 

[Ray Vickson]

Homework Statement

View attachment 83171

Homework Equations

Laplace Trasformations

The Attempt at a Solution

a. done
b. f(t)= t -3*t*u(t-1) + 4*u(t-1) -3*u(t-2) -2*t*(t-2)
c. 1/(s^2) - (3e^-s -2e^-2s)/(s^3) + (4e^-s -3e^-2s)/s
d. 1/(s-1) * (1/(s^2) - (3e^-s -2e^-2s)/(s^3) + (4e^-s -3e^-2s)/s)

These are the answers i got but my friend got all different ones and we are not sure who is correct. Thanks for any help.

The first 4 terms on the right of (b) are OK but the fifth term is incorrect. You should develop the habit of always checking these things for yourself; just look at f(t) and your right-hand-side for 0 < t < 1, then for 1 < t < 2, then for t > 2. What does your answer in (b) look like for t > 2?