u6 



KINEMATICS. 



[214. 



i/= cos 27T--; 



[ 27T--4;) 

 \ i6/ 



Similarly the next point 



is found from the next two points of division on the circles, etc. 

 To construct the dotted curve, it is only necessary to begin 

 on the circle over AB with D as first point of division. 



214. Exercises. 



(1) With the data of Art. 213 construct the curves for phase differ- 

 ences of 2/12, 3/i2, 11/12 of the smaller period. 



(2) Construct the curves (Art. 212) 



x = a cos to/, y = a cos(2o>/ + S) 



for 8= O, 7T/4, 7T/2, 37T/4, TT, 511/4, 3W/2, 771/4, 27T. 



(3) Trace the path of a point subjected to two circular vibrations of 

 the same amplitude, but differing in period, (a) when the sense is the 

 same; (b) when it is opposite. 



215. The mathematical pendulum is a point compelled to move 



in a vertical circle under the 

 acceleration of gravity. 



Let <9 be the centre (Fig. 52), 

 A the lowest, and B the highest 

 point of the circle. The radius 

 OA = loi the circle is called the 

 length of the pendulum. Any 

 position P of the moving point 

 is determined by the angl< 

 AOP = 6 counted from the ver- 

 tical radius OA in the positiv< 

 (counterclockwise) sense of rota- 

 tion. 

 If P Q be the initial position of the moving point at the time 



