The Maths

A simple mathematical expression accounting for the sinusoidal displacement of the cell array along the x axis with respect to a fixed reference frame (e.g., the MSG WV) can be cast in compact form as:

s^lab(t)=b sin(ω t) n                      (1)

where b is the amplitude, ω=2πf is the angular frequency of the displacement and n is the unit vector along the direction of vibrations. The ensuing time-varying acceleration can be derived mathematically by taking the second derivative of eq. (1) with respect to time, i.e.

g(t)=g_ωsin(ω t)n where g_ω=bω²                         (2)