Since complex waveforms can be represented as a series of sines or cosines, we can study the response of the accelerometer to a periodic input to determine its frequency response. Therefore, let the object to which the accelerometer is attached undergo the following displacement:
(1)
By differentiating Equation 1 twice with respect to time, the accelerometer's housing experiences an acceleration of:
(2)
Recalling Equation 2 from the Theory of Operation and substitiuting Equation 2 from above, the governing equation of the primary transducer within the accelerometer is:
(3)
It can be shown that the solution to Equation 3 is given by:
(4)
where the amplitude response, C', is given by:
(5)and the phase response, [[phi]], is given by:
(6)