(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hello all,

Having difficulty with this one question that involves complex roots. Here it is:

[tex]F(s)=\frac{s+3}{s^3+3s^2+6s+4}[/tex]

I tried two different ways to tackle it. First method I divided it right away:

[tex]F(s)=\frac{s+3}{s^3+3s^2+6s+4}\rightarrow{s^2+6-\frac{14}{s+3}}[/tex]

Is there some sort of approach to something like s^2? I have not taken a differential equations course, and this is in one of my classes for modelling circuits.

If I decide not to do it this way, I can break it up via partial fractions:

[tex]F(s)=\frac{s+3}{s^3+3s^2+6s+4}=\frac{s+3}{(s+1)(s+1-\sqrt{3}j)(s+1+\sqrt{3}j)}=\frac{A}{s+1}+\frac{B}{s+1-\sqrt{3}j}+\frac{C}{s+1+\sqrt{3}j}[/tex]

where j is a complex number.

Thus,

[tex]A(s^2+2s+4)+B(s+1)(s+1+\sqrt{3}j)+C(s+1)(s+1-\sqrt{3}j)=s+3[/tex]

[tex]As^2+Bs^2+Cs^2=A+B+C=0[/tex]

The part that I do not know how to do is from here.

Would it be:

[tex]2As+2Bs+2Cs+j\sqrt{3}Bs+j\sqrt{3}Cs=s[/tex]

or are the complex numbers treated separetely?

Or is there an easier way, altogether?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Inverse Laplace Transform

**Physics Forums | Science Articles, Homework Help, Discussion**