2I3-] 



PLANE MOTION. 



In tracing these curves, imagine the simple harmonic motions 

 replaced by the corresponding uniform circular motions (Fig. 

 51). With the amplitudes 6, 5 as radii, describe the semi- 

 circles ADB, AEC, so that BC is the rectangle within which 

 the curves are confined ; the intersection of the diagonals of 

 this rectangle is the origin O, AB is parallel to the axis of x t 

 AC to the axis of y. Next divide the circles over AB, AC into 

 parts corresponding to equal intervals of time. In the present 

 case, the periods for AB, AC being as 3 to 4, the circle over 



Fig. 51, 



AB must be divided into 3/2 equal parts, that over AC into 

 4 . In the figure, n is taken as 4, the circles being divided 

 into 12 and 16 equal parts, respectively. 



The first point of the full drawn curve corresponds to ^=o, 

 that is x=6,y = $ ; this gives the upper right hand corner of 

 the rectangle. The next point is the intersection of the vertical 

 line. through D and the horizontal line through E, the arcs 

 BD=i/i2 of the circle over AB, and CE=i/i6 of that over 

 AC being described in the same time, so that the co-ordinates 

 of the corresponding point are 



