APERIODIC MOTION. 31 



equilibrium ; we have then for / = 0, x a and = 0. We get from 

 this, 



27 



V--a ~ 

 " ~ 



27 

 and therefore 



(25) x = e~ et \U + 7) #t - ( - 7) *-y'l . 



27 J 



In this case, the deflection represented in rectilinear co-ordinates 

 as a function of the time, is equal to the difference of the ordinates 

 of two experimental curves which approach asymptotically the axis of 

 the abscissae. The value of x only becomes null, for /= QO . 



686. Instead of leaving the system to itself when it makes an 

 angle a, let us suppose that we give it an angular velocity o> directed 

 towards the position of equilibrium. 



In this case the constants A and A' of the equation become 



2J 27 



which gives 



(26) X = - - | [a(e + 7) - to] 0* - [a(e - 7) - w] *~>f j . 



The motion is still aperiodic; but if the original velocity is 

 suitable the system may pass beyond its position of equilibrium. 

 The time of the passage through this position is defined by the 

 equation 



/ = T / fa> ~ cc ( e ~y). 



27 ' o>-a 



