﻿160 Harmonic Analysis of Motion 



t; 



2 



Since <fi lies between +— and — - , and n<l, 



2icf> = log (l_^-^)_log (1 -ne iQ ) 

 = -ne- ie -±n 2 e- 2i9 - : k,nh- 2>i9 -... 



+ ne ie + We 2ie + ^nh™ +'... 

 = n . 2z sin + in 2 . 2z sin 20 + Jn 3 . 2i sin 3(9 + . . . . 



<£ = ttsin0 + in 2 sin20+§n 3 sin30 + (8) 



^ = (?icos0 + n 2 cos20 + n 3 cos30 + ...)^. . • (9) 



^ = (_» sin 0~2n 2 sin 20- 3n 3 sin 30-...) fc 



. . ! (10) 

 R* 3. 





4. In the Pin and Slot mechanism (fig. 3) we have 



"\|r = IT — — (£. - 



The angle <£ is given by (8), so that 



n ii 



^ - rjr-O-n sin 0- T sin 20-^- sin 3(9- ..., (11) 



<i± _ _^ (1 + n C os (9 + 7i 2 cos 2(9 + n 3 cos 30 + ...), (12) 

 ttt etc 



^ = (~ V (n sin + 2n* sin 20 ■+ 3?* 3 sin 30+ ...). (13) 



It will generally be found that we need to consider but 

 the first few terms of these series in making numerical 

 calculations. 



