  We consider a tapping dynamics, analogous to that in experiments on granular
media, on spin glasses and ferromagnets on random thin graphs. Between taps,
zero temperature single spin flip dynamics takes the system to a metastable
state. Tapping, corresponds to flipping simultaneously any spin with
probability $p$. This dynamics leads to a stationary regime with a steady state
energy $E(p)$. We analytically solve this dynamics for the one dimensional
ferromagnet and $\pm J$ spin glass. Numerical simulations for spin glasses and
ferromagnets of higher connectivity are carried out, in particular we find a
novel first order transition for the ferromagnetic systems.
