SEISMIC METHODS 927 



Corresponding to these assumptions, the equation of motion of the 

 vibrating element is rf 



d X dx 



m -jiT -^ K—7-+ ex = P sin w/ 

 dt" dt 



where m = mass of vibrating element = mass of oscillator plus a small 

 amount of soil directly under the oscillator. 

 X = amplitude of vibration. 

 t = time. 

 K = coefficient of friction. 

 c = elastic coefficient (force in pounds required to deflect the 



system one inch). 

 CO = frequency of oscillator. 

 P sin (tit = centrifugal force of rotating disc oscillator. 



The maximum amplitude a of the disturbance is given by the equation : 



P 



a = - 



wy (wo" — (0")^ + 48-w- 



where wq = natural frequency of the vibrating element 



8 = damping = ^ 



The phase difference <j> between the exciting force and the amplitude 

 of the motion is given by the relation 



28(0 

 tan <j> = — ^ 



(OQ to" 



The resonance point of the soil adjacent the oscillator may be deter- 

 mined by measuring the amplitude of the motion — as recorded by a 

 seismograph located near the oscillator — for various frequencies, i.e., for 

 various values of co and by plotting an amplitude versus frequency curve. 

 The resonance frequency may also be determined by measuring the settling 

 or movement of the oscillator for various frequencies of the oscillator and 

 plotting a settlement versus frequency curve. 



The empirically established correspondence between natural frequency 

 and bearing capacity or allowable soil pressure is given in Table 25. 



The soil adjacent the oscillator will be set into vibration at its natural 

 or resonance frequency for a particular value of the oscillator frequency. 

 However, this soil, as well as the remainder of the soil constituting the 

 elastic medium, will undergo forced vibrations for any frequency of the 

 oscillator. 



Corresponding phases of the waves impinging on two seismometers 

 located at different distances from the oscillator arrive at different times. 

 Hence, the velocity of the wave in the soil under investigation can be 



t cf. p. 788. 



