- #1

member 731016

- Homework Statement
- please see below

- Relevant Equations
- Please see below

For this problem,

The solution is,

However, I'm confused by the partial fraction decomposition of ##\frac{2}{s^4(s^2 + 1)}##

I never done that sort of thing before. However, I think it would be done like this (Please correct me if I am wrong, the algebra is crazy here).

##\frac{2}{s^4(s^2 + 1)} = \frac{A}{s} + \frac{Bs + C}{s^2} + \frac{Ds^2 + Es + F}{s^3} + \frac{Gs^3 + Hs^2 + Js + K}{s^4} + \frac{Ls + M}{s^2 + 1}##

It seems rather tedious because of the ##\frac{1}{s^4}##, but is that correct (There may be a simpler method but I can't see it).

Thanks!

The solution is,

However, I'm confused by the partial fraction decomposition of ##\frac{2}{s^4(s^2 + 1)}##

I never done that sort of thing before. However, I think it would be done like this (Please correct me if I am wrong, the algebra is crazy here).

##\frac{2}{s^4(s^2 + 1)} = \frac{A}{s} + \frac{Bs + C}{s^2} + \frac{Ds^2 + Es + F}{s^3} + \frac{Gs^3 + Hs^2 + Js + K}{s^4} + \frac{Ls + M}{s^2 + 1}##

It seems rather tedious because of the ##\frac{1}{s^4}##, but is that correct (There may be a simpler method but I can't see it).

Thanks!