How to Derive the Equation for an RLC Circuit?

[Ai En]

how to get this equation:
Vout/Vin = [RL]/[-[ω][/2]+jω(R/L)+1/(LC)]

 

[a-tom-ic]

- Show us the picture of the RLC Circuit your using.
- Tell us how Vout is defined.
- Tell us what [omega][/2] stands for (use the boards LaTeX syntax).

 

[Ai En]

http://upload.wikimedia.org/wikipedia/en/1/14/RLC_series_band-pass.svg

 

[a-tom-ic]

Hi Ai En,

as a solution you could use the voltage divider formula to get a first equation:
$$\frac{V_{out}}{V_{in}} = \frac{R_L}{R_L + j \omega L + \frac{1}{j \omega C}}$$

afterwards if you think that's useful you can try to manipulate this formula until you get the one given to you. Since i can not interpret your given equation (as i said use the LaTeX encoding to be more clear about your formula) i can only guess and did for example multiply the whole formula with $\frac{j \omega L}{j \omega L}$ and the denominator again with $\frac{L}{L}$ that results in:
$$\frac{V_{out}}{V_{in}} = \frac{j \omega R_L}{L \cdot \left( - \omega^2 + j \omega \frac{R_L}{L} + \frac{1}{C L}\right)}$$