Factoring Problems: Solving for Inverse-Laplace Transformation

[EvLer]

How can i factor this nicely, so that i can get a form to inverse-laplace transform it

$$\frac{0.25s}{s^2+0.25s+0.25}$$

so far i get this in denominator: $$(s+\frac{1}{8})^2+\frac{15}{64}$$

after completing the square, but then the last fraction is not a square of anything... and i need a square there, the way everything else looks...

 

[CarlB]

The denominator is already a square. I don't see how you got the other stuff. The answer should be a simple polynomial multiplied by an exponential.

Carl

 

[EvLer]

I don't see a square there, if $$(a+b)^2 = a^2+2ab+b^2$$

this is a simple algebra thing... i guess I'm not seeing it could you show please?

 

[ehild]

How can i factor this nicely, so that i can get a form to inverse-laplace transform it

$$\frac{0.25s}{s^2+0.25s+0.25}$$

so far i get this in denominator: $$(s+\frac{1}{8})^2+\frac{15}{64}$$

after completing the square, but then the last fraction is not a square of anything... and i need a square there, the way everything else looks...

Do not panic. 15/64 is the square of

$$\frac{\sqrt {15}}{8}$$

ehild

 

[CarlB]

I don't see a square there, if $$(a+b)^2 = a^2+2ab+b^2$$

this is a simple algebra thing... i guess I'm not seeing it could you show please?

My mistake. I don't see anything wrong with the way you're doing this problem, so far.

Carl