ISOCHRONOUS OSCILLATIONS. 1 9 



from this we have 

 (4) 







sm nt, 

 n 



dx 







The value of the angle of deviation a, which corresponds to =0, 

 in which nt = - , is 



(5) 2 .-?. 



The first elongation is attained at the end of a time 



7T TT 



nt = - or / = ; 



2 2^ 



the following ones at the times 



37T 57T TTT 



2H ' 2H ' 2W ' ' 



The interval between two consecutive elongations is constant ; 

 the time of oscillation is constant, and its value is 



This duration is independent of the amplitude ; the oscillations are 

 said to be isochronous. 



The conditions of the problem that is to say, the value of w, 

 which gives the ratio of the directing couple to the moment of 

 inertia, and the angular velocity of the system cu may be deter- 

 mined by the investigation of the motion ; that is, deduced from 

 the time of oscillation T, and from the angle of deviation. We have, 

 in fact, 



7T 



n = 



T' 



(7) 



(0 = an = a 

 C2 



