ACCELERATION EFFECTS ON ELECTRON TUBES 1207 



system formed by the stiff active element K2 and the retaining spring Ki. 

 For negligible damping in these springs the motion of the mass relative 

 to the base is : 



yi = ^^.•Sm«< (2) 



1 



\ 



(.")■ 



Here ccn = the natural circular frequency of the mass on the springs. The 

 force F exerted by the springs on the mass is: 



(i^i + K2)Xo(-Y 



F = {K^ + K2)y, = / sT Sin c^t (3) 



The accelerometer is constructed so that the spring constant Ki of the 

 retaining spring is considerably smaller than that of the active element 

 Ki. Therefore, for vibration frequencies relatively low as compared to co„, 

 equation_^(3) becomes: 



K2 2 

 F = ~2 Xqo) Sin cot 



Where (4) 



K2 2 



— = M, and Xquo Sin iot = a 



The stress produced by this force F produces a charge on the active ele- 

 ment which is proportional to the instantaneous value of the acceleration 

 to which the unit is subjected. Properly calibrated therefore, the acceler- 

 ation can be measured in gravitational units. When the disturbing force 

 consists of a number of these components; the total instantaneous output 

 is proportional to the sum of these components, within the frequency 

 limitation of the pick-up. 



In deriving the above expressions, a number of assumptions have been 

 made. Equation (4) therefore holds only if: 



(a) co„ is made large compared to the highest shock or vibration fre- 

 quencies that are to be recorded. 



(b) Ki is small compared to K2. Since the function of the retaining 

 spring is merely to hold the assembly together for peak accelerations 

 encountered, a soft spring with a sufficiently large static deflection can 

 be employed or the spring may be replaced by conducting cement to 

 hold the parts together. 



