MATHEMATICAL APPENDICES. 201 



Equating the imaginary parts, we get 



J ? sin ptdt = -V- |T sin 4?* - p cosj 



C' being a constant 



rt 



L^ 



;= S7i sin (^ - ^) + C" ( 3 ) 

 where 



tan0=^ 

 r 



Substituting this value of the integral in (2) we get, after dividing 

 bye?- 



As increases e~ r rapidly diminishes and tends towards the 

 value zero, so that a steady periodic state is given by the 

 equation 



_ e sin (pt - 0) 



APPENDIX C. 



Solution of the equation (see 24, Chap. IV.) 

 T dH di i 



L di* +r dt + c = pecospt < 



The simplest method of solution here is to assume that i is of 

 the form 



i = I sin (pt 0) 

 so that 



s= ->* 



