- #1
lpau001
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Homework Statement
Use the First Shifting Theorem (translation on the s axis) to find f(t).
L-1[(2s-1)/(s2(s+1)3]
Homework Equations
The Attempt at a Solution
This is going to take forever.. Can we assume that I am putting the L^-1 all over the place?
[(2s-1)/(s^2(s+1)^3)] = [(2(s+1)-3)/(s^2(s+1)^3)] */ on this step I don't know how to change the s^2 in the denominator to an (s+1)^2 form.. do I need too? /*
[(2[STRIKE](s+1)[/STRIKE])/(s^2(s+1)[STRIKE]3[/STRIKE]2)] - [3/(s^2(s+1)^3)]
Then using partial fractions */ This is where I get confused /*
(As+B)/(s^2) + C/(s+1) + (Ds+E)/(s+1)^2 = (2s-1)/(s^2(s+1)^3)
solving coefficients (after a lot of math)
A=5 B=-1 C=-3 D=-2 E=-6
Putting coefficients back into problem..
(5s-1)/s^2 + (-3)/(s+1) + (-2s-6)/(s+1)^2
Attempted solution..
[(5s)/(s^2) - (1)/(s^2)] + [-3/s|s+1] + [-2s/s^2|s+1] + [-4/s^2|s+1]
I get...
5 - t - 3e^-t - 2e^-t - 4te^-t
Which is wrong. I'm close, kinda, I believe I erred in my partial fractions set up, but any help would be so nice.. Thanks PF.