Partical Fractions

krnhseya

1. The problem statement, all variables and given/known data

Turn this into partial fraction.
k1b1/[((k1+b1*s)(k2+b2*s))-b1[tex]^{2}[/tex]s[tex]^{2}[/tex]]

2. Relevant equations

n/a

3. The attempt at a solution

original question was to find the transfer function with springs and a damper and I reduced it to this far but I cant get the partial fraction.
once i get that partical fractions, i take the inverse laplace transform and get the answer.

rocomath

I'm getting dizzy reading it ...

[tex]\frac{k_1b_1}{(k_1+b_1s)(k_2+b_2s)-b_1^2s^2}[/tex]

Yes?

krnhseya

yeap :)

krnhseya

well is this impossible to separate?
i did other problems but i am just stuck on this one.
let me know if you need the actual problem statement...

HallsofIvy

you want, of course, to factor the denominator. I think I would be inclined to multiply out that first part and combine coefficients of like powers. It will be, of course, a quadratic. At worst, you could set the denominator equal to 0 and solve the equation by the quadratic formula.

tiny-tim

[tex]\frac{k_1b_1}{(k_1+b_1s)(k_2+b_2s)-b_1^2s^2}[/tex]

krnhseya, just expand the bottom line into the form [tex]as^2\,+\,bs\,+\,c[/tex], and then factor it using the good ol' (-b ±√b^2 - 4ac)/2a.

krnhseya

well that b1 squared and s squared at the end...it cancells the expansion of the squared part...

tiny-tim

No, it doesn't …

It's [tex]k_1k_2\,+\,(b_1k_2\,+\,b_2k_1)s\,+\,b_1(b_2\,-\,b_1)s^2[/tex]