It can be shown that . . .

(1")                              

where:

a is the acceleration of the mass, m.

The forces imposed on the seismic mass are given by:

(2")                       
(3")                       
(4")                   

The acceleration of the accelerometer housing is defined as:

(5")                                    

Substituting into Equation 1":

(6")         

(7")                   

Dividing Equation 7" by k, yields:

(1)