686 SEISMIC METHODS [Chap. 9 



T=- = ^; loger = ^. (9-87d) 



e Ae T 



In seismograph calibration it is convenient to use the relative damping 

 ri, which is the ratio of damping constant and natural frequency wo and 

 varies therefore from for no damping to 1 for critical damping. Hence, 



Wo Jo 



In Galitzin's publications a damping factor fj. is used. This is equal to 

 the ratio of damped and undamped frequency: 



/x = ^^=-^= Vr:^^. (9-87/) 



«o Jo 



5. Forced oscillations; steady state conditions. Generally the ground 

 continues to move after the seismograph motion has started. The two 

 motions will be superimposed on each other. Expressions may be derived 

 for the resultant "forced" oscillations, provided that certain simplifications 

 are introduced. Replacing the on the right side of eq. (9-846) by a 

 term containing the acceleration x of the point of suspension, 



d + ojoa = - Vx. (9-88a) 



It is seen that a seismograph can be made to record the ground motion 

 perfectly if the pointer acceleration equals magnified ground acceleration, 

 that is, if d = — Vx. This condition can exist only if wo = and if the 

 seismograph has an infinitely long period, that is, if it is astatized. Ac- 

 tually zero frequency is mechanically impossible; however, the lower the 

 natural frequency, the more the second time derivative of the recorded 

 amplitude will correspond to the ground acceleration. The seismograph 

 is essentially a displacement recorder. Conversely, if a seismograph is 

 made with a natural frequency much higher than that of the ground 

 motion, a is negligible compared with woa and eq. (9-88a) becomes a = 

 (— V/ajo).T. It is seen that the recorded amplitude is proportional to the 

 ground accelerations and that, therefore, the seismograph is an acceler- 

 ometer. However, the ground accelerations are recorded with a reduced 

 magnification (V/wo). 



A definite solution of eq. (9-88a) can be given if a time function of a; is 

 introduced, the simplest assumption being a continuous harmonic function. 

 Hence, ii x = X sm at (where X is the maximum amplitude and w is 

 ground frequency), x = —X(a sin wt, and eq. (9-88a) becomes 



d + wla = WX(a sin coi, (9-886) 



