  We examine the dynamical magnetic response of the underdoped cuprates by
employing a phenomenological theory of a doped resonant valence bond state
where the Fermi surface is truncated into four pockets. This theory predicts a
resonant spin response which with increasing energy (0 to 100meV) appears as an
hourglass. The very low energy spin response is found at (pi,pi +- delta) and
(pi +- delta,pi) and is determined by scattering from the pockets' frontside to
the tips of opposite pockets where a van Hove singularity resides. At energies
beyond 100 meV, strong scattering is seen from (pi,0) to (pi,pi). This theory
thus provides a semi-quantitative description of the spin response seen in both
INS and RIXS experiments at all relevant energy scales.
