784 EXPLORATION GEOPHYSICS 



Alt' 

 Replacing n in Equation 128 y = — -— y 



Equation 128 may be used to compute the displacement for a specified acceleration. 

 Referring to Figure 475, if there is not an outside impressed acceleration, Equation 125 

 may be written as 



y+f-y = (130) 



M 



Substituting for y the value given by Equation 128, 



^-■^ (131) 



T = 2.M=2.^^J^ 



In the theory of the mechanics of vibrating particles, the definition of the equivalent 

 pettdulum length is given by 



L.^^^-P (132) 



Air" 



For any oscillatory system of motion of period T, it is in general possible to com- 

 pute by use of Equation 132 the length of a theoretical pendulum which would oscillate 

 with the same frequency. 



Applying this equation in our case of the loaded spring, the equivalent pendulum length 

 is equal to L — Lo, or the elongation of the spring due to loading. From this it is 

 evident that the arrangement shown by Figure 475 is suitable for short periods only, 

 because long periods would make necessary the use of a very long spring. This places 

 a practical limitation on this type of arrangement. 



In the theory as developed thus far, the damping of the system has not been con- 

 sidered. An oscillating mass which is under the influence of an outside force (such as 

 that due to the motion of the ground), in addition to the force tending to drive the 

 mass to the rest position, is said to be executing a forced vibration. In the case of 

 seismology the geophysicist is particularly interested in the nature of this so-called 

 outside force. To state the matter more exactly, the geophysicist is interested in the 

 ground motion from which this force is a consequence. Now an undamped seismometer 

 (not under forced vibration) will for the most part vibrate at a frequency known as 

 free resonance when subjected to a transient pulse. In other words, the pendulum of 

 an undamped system will not follow through the motions impressed on it. It will 

 record the instant of disturbance but will continue to vibrate after the disturbance 

 has passed. 



In seismology a usable representation of the motion of the ground must be obtained. 

 Therefore it becomes obvious that, in so far as practical, it is necessary that the 

 suspended mass follow the forced vibrations impressed on the seismometer rather than 

 any free oscillatory motion inherent in the mechanism. 



To eliminate the free motion of the seismometer system provision should be made 

 for damping whereby the free motion is absorbed by doing work. In Figure 475 a 

 dash-pot of viscous liquid is illustrated schematically for this purpose. The viscous 

 medium is usually oilf, but the more modern damping arrangements are generally 

 electromagnetic in nature, to avoid the varying viscosities of liquids with changes of 

 ambient temperature. Electromagnetic damping efifects are nearly independent of tem- 

 perature changes. 



t The relatively large temperature-viscosity variations of practically all suitable fluids necessitate 

 a change to light oil in the colder months, and heavier, more viscous oils in the hotter months. 



