792 EXPLORATION GEOPHYSICS 



and 



W = m^l^th*!L t (152) 



It is of some interest in the theory of vertical load spring pendulums that the energy 

 supplied by the applied force is equal to that necessary to overcome the damping resis- 

 tance of the system. It then should follow that the value of the work {W) should also 

 be calculable as the necessary work done against the force of damping. 



dW =Kydy 



W = 2mnh\^^ dt 

 dt dt 





= 2ntnh \ y' dt 



K F 



where 2hn = — and rv' = — 



m M 



The kinetic energy by definition is £ = — — or for the case under consideration 



m ^ 

 2 



Then 



W = Anh \ E dt = AnhE t 

 From Equation 150 



= 4«A I Edt = ' 



Tzr ma'zir'hnt 



which is the expression of Equation 152. 



Effects of Natural Frequency of Seismometer. — To examine the effect of the 

 magnitude of the period of the oscillating system of a seismometer, the equation for a 

 damped linear oscillator may be used. 



y = — 2nhy — n'y — Z (126) 



If the period is very great, then the coefficient (n) would be very small and the terms 

 containing this coefficient may become unimportant. Equation 126 might reduce to an 

 expression similar to 



y = -Z 



This would mean that the oscillating particle would practically duplicate the impressed 

 motion, and the displacement of the particle would be proportional to the displacement 



