43] 



LOGARITHMIC DECREMENT. 



151 



The smaller the damping ?c, the more nearly does the time of the 

 maximum coincide with that of the maximum of the cosine factor 

 in 33). In any case successive maxima follow each other at intervals 

 equal to the period of the oscillation , 



36) T = ^ 



At two successive maxima on the same side, s 1 and S 2 , the cosine 

 term will have the same value , therefore the ratio of the elongations 

 will be that of the exponential factors , or 



Fig. 32. 



The logarithm of the ratio, 

 37) (5 = ^^ 



-1 



is accordingly constant, and by means of observations on the loga- 

 rithmic decrement we may determine the damping. We see that the 

 decrement depends on and increases with the ratio of the square of 

 the coefficient of damping % to the coefficient of "stiffness" I?. 



If there were no damping, B = 0, we should have for the period, 



Introducing these values of T and d, we may write 

 38) T = 



