On the other hand, the maximum amplitudes (or accelerations) undergone by a given
vibrating foundation can be determined by the principles of soil dynamics. Analytical
formulations available from such analyses are provided in the ensuing sections for a
number of different modes of vibration.
3.5.1 Vertical Steady-State Vibrations
The equation of motion for a rigid foundation of mass m subjected to a vertical steadystate
constant amplitude simple harmonic force can be written as (Lysmer, 1966)