1206 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1953 



encountered humidity and temperature conditions. Accelerometers ap- 

 proximating the size and weight of electron tubes are now commercially 

 available and used for measuring accelerations imparted to tubes through 

 their sockets. 



By proper construction the voltage output of these pick-ups is pro- 

 portional to the stresses induced in the active elements within the desired 

 frequency range. Depending on choice of material and construction, their 

 active elements can be used in compression, shear, or torsion. Fig. 1(a) 

 shows the simplified construction of a compression type pick-up. It 

 consists of (1) a base which is rigidly fastened to the point at which ac- 

 celerations are to be measured, (2) a sensitive element, (3) a weight, and 

 (4) a retaining spring. The whole assembly is shown held together by a 

 screw. The mechanical equivalent of this structure is shown in Fig. 1(b). 



When this unit is subjected to sinusoidal motion its displacement is 

 given^^by 



X = Xo • sin £0 • i 



Where X 

 at time t 



instantaneous displacement of the base from equilibrium 



Xo = maximum displacement from equilibrium 

 CO = circular frequency of the motion 

 The instantaneous acceleration then becomes 



dx 

 a = 3-r = — Xqw^ Sin (at 

 at- 



(1) 



The motion is transmitted to the mass M through the parallel spring 



RETAINING 

 SPRING (4) ^- 



MASS (3)-^^^ 



ACTIVE "^ 



ELEMENT (2) ~* 



BASE(1). 



'm^m^ -tx 



(a) 

 Fig. 1 — Compression type accelerometer (a) and its mechanical equivalent (b). 



