This harmonic oscillator is driven and damped, with the form:
$$\ddot{x} + \lambda \dot{x} + \omega_0^2 x = A \cos(\omega_d t)$$
Now, I have used the ansatz (guess): $x(t) = B \cos(\omega_d t + \phi)$, and have written B in the form:
$$B = \frac{A} {\sqrt{(\omega_o^2-\omega_d^2)^2+\lambda\omega_d^2}}$$
Next, I am required to "approximate B using the Lorentzian form"
$$B = \frac{C}{(\omega_d - \Omega)^2+\biggl(\frac{\Gamma}{2}\biggr)^2}$$
However, this is where I am stuck. I know that because it says "approximate" I will somehow have to drop out terms from my first expression to B, but I don't know where to start. How can I write B in this form?
EDIT: I have found a wikipedia article on resonance which show a form very similiar to what I seek, however, I can't seem to find a derivation http://en.wikipedia.org/wiki/Resonance