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## Homework Statement

I have this lowpass circuit which I have transformed to the S-domain.

The circuit is to be exposed to a unit step, and then I shall convert the transient response to the time domain.

Here's the transfer function of the lowpass circuit:

[tex]H(s) = \frac{\frac{1}{LC}}{s^2 + s \frac{1}{RC} + \frac{1}{LC}}[/tex]

[itex]\frac{1}{LC} = 1000000[/itex]

[itex]\frac{1}{RC} = 0,001415[/itex]

The function of the unit step is

[tex]x(t)=1 --> X(s) = \frac{1}{s}[/tex]

## Homework Equations

[tex]

Y(s) = H(s) * X(s)

[/tex]

[tex]

Y(s) = \frac{\frac{1}{LC}}{s^2 + s \frac{1}{RC} + \frac{1}{LC}} * \frac{1}{s}

[/tex]

## The Attempt at a Solution

Now, my problem is that I have great difficulties "arranging" the equation before converting it back to the time domain.

I know that it involves some partial fractions and some unknows (A, B, C and so forth), but even though I have studied the relevant subject in my text book, I cant f*cking do it.

I'll show you what I got so far (wrong as it may be)

[tex]

1: \frac{A}{s} * \frac{B}{s^2 + s \frac{1}{RC} + \frac{1}{LC}} = \frac{\frac{1}{LC}}{s*(s^2 + s \frac{1}{RC} + \frac{1}{LC}})

[/tex]

[tex]

2: A*(s^2 + s \frac{1}{RC} + \frac{1}{LC}) + Bs = 1

[/tex]

I feel that I'am wondering in the dark, so if someone could point me in the right direction or even shed some light over what I am doing and how I am suppose to do it I would be very very happy :)