THE MEASUREMENT OF CURRENT 29 



where 



~W 



In this case, the final deflection is attained by a series of 

 oscillations. If the values of Wi and w 2 are substituted in (10) 

 and the resulting equation simplified by the use of the exponential 

 values of the sine and cosine and the relation 



A sin ft + B cos ft 

 it will be found that 



(16) 



The variable part of (16) represents an oscillation of con- 

 stantly decreasing magnitude and having a period, 



(17) 

 4P 2 

 The time of a complete swing when no damping is present is 



To = 

 So 8 = 6,- 6, I "" sin |^ < -f tan- 1 ^ | (18) 



The elongations, or maximum and minimum values of the 

 deflection, occur when 



T T 



If, when the needle is at rest in its deflected position, the 

 circuit is broken, the return to zero is by a series of oscillations 

 according to the equation 



^' ~ 



(19) 



T ^' r2ir irP~\ 



6 = e " To ^ Sin L T * + tan " 1 IcT J 



Equations (18) and (19) are plotted in Fig. 13 where the values 

 T = 0.2, P = 0.2 and k = 0.1 are assumed. 



