  We present results on the dynamics of the distorted diamond chain, S=1/2
dimers alternating with single spins 1/2 and exchange couplings $J_1$ and $J_3$
in between. The dynamics in the spin fluid (SF) and tetramer-dimer (TD) phases
is investigated numerically by exact diagonalisation for up to 24 spins.
Representative excitation spectra are presented, both for zero magnetic field
and in the 1/3 plateau phase and the relevant parameters are determined across
the phase diagram. The behavior across the SF-TD phase transition line is
discussed for the specific heat and for excitation spectra. The relevance of
the distorted diamond chain model for the material Cu$_3$(CO$_3$)$_2$(OH)$_2$
(azurite) is discussed with particular emphasis on inelastic neutron scattering
experiments, a recent suggestion of one possibly ferromagnetic coupling
constant is not confirmed.
