We consider some of the conditions associated with ergodicity-breaking and vitrification, in particular the equivalent, in quench vitrification, of the ωτ=1 condition that is well-known in relaxation spectroscopy. For a given quench rate, Q=dT/dt, strong liquids are trapped at much higher temperatures, relative to Tg, than are fragile liquids. We relate the trapping of the system during quenches to the multidimensional 'energy landscape' by means of which the configurational microstates of the system are defined. To characterize the energy landscape at energy levels that are usually associated with fluid materials, we use differential scanning calorimetry on hyperquenched glasses. This yields not only the excess potential energies of the states trapped-in during quench Q, but also the trap depths. The latter are found to be much smaller, relative to kTg, for strong liquids than they are for fragile liquids.