def dhoModel(w, Gamma0, I0, Gamma, I, Omega):
    """
    Defines the damped harmonic oscillator model for S(q,w)/S(q)

    This is to be used at a specific q, which can then be used to build all
    the parameters as functions of q

    S(q,w)         1/2 Gamma0(q)                   Omega(q) Gamma^2(q)
    ----- = I0(q)----------------- + I(q)-------------------------------------
     S(q)        w^2 + (Gamma0/2)^2      (w^2 - Omega^2(q))^2 + (w Gamma(q))^2
    """

    return I0 * 0.5 * Gamma0 / (w**2 + (0.5 * Gamma0)**2) \
        + I * Omega * Gamma**2 / ((w**2 - Omega**2)**2 + (w * Gamma)**2)