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:
slab(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)=gωsin(ω t)n where gω=bω2 (2)