# Laplace transform

## Homework Statement

I already got Q(s)=150/(s(s^2+20s+200)), then i complete the square on the quadratic.
I got Q(s)=150/(s((s+10)^2+10^2))). But then i cant find the Q(t) because the equation (s+10)^2+10^2=0 dosent have roots. Or i have to use complex numbers ? So I am confused.

## The Attempt at a Solution

vela
Staff Emeritus
Homework Helper
Did you use partial fractions to get separate terms first?

To get the inverse, look at the Laplace transforms of sine and cosine.

Did you use partial fractions to get separate terms first?

To get the inverse, look at the Laplace transforms of sine and cosine.
U mean use partial fractions on s(s^2+20s+200)? but how?

I can get 150/s * 1/((s+10)^2+10^2), but this dosent seems to fit either sin or cos

vela
Staff Emeritus
Homework Helper
You need to use partial fractions to separate it into terms that appear in the tables.

$$\frac{150}{s(s^2+20s+200)} = \frac{A}{s} + \frac{Bs+C}{s^2+20s+200}$$

Solve for A, B, and C.

You need to use partial fractions to separate it into terms that appear in the tables.

$$\frac{150}{s(s^2+20s+200)} = \frac{A}{s} + \frac{Bs+C}{s^2+20s+200}$$

Solve for A, B, and C.
thanks for reply, after i solve partial fraction what should i do?
I solved: which = 3/40s + ((-3s/40-3/2))/(s^2+20s+200)

vela
Staff Emeritus
Homework Helper
$$\frac{150}{s(s^2+20s+200)} = \frac{A}{s} + \frac{B'(s+10)}{(s+10)^2+10^2} + \frac{C'}{(s+10)^2+10^2}$$