48 



MOTION IN TEEMS OF ACCELERATION. [CHAP. IV. 



circle, and when the moving point is at N on one diameter of 

 this circle, so that ON x, draw NP at right angles to this 

 diameter, and consider the motion of the point P. 



Fig. 32. 



Let the angle NOP = 0. 



Then x, = a cos 0, and y, = a sin 6, are coordinates of P. 



By differentiating we have 



x = a sin 6 6, x a sin 6 a cos 2 

 hence = -?/0 + #0 2 ; 



snce 



x = 



we must have 



= 0, and 2 = p. 



Hence the point P describes the circle uniformly ; the angular 

 velocity of the radius vector is uniform and equal to V/^ an d the 

 angle 6 = t V/*- 



The distance of the point N from at time t is given by 

 x = a cos 



The velocity of the point is directed along xO, and its magni- 

 tude is a \J[j, sin (t\/fj,). 



The above process shows that the solution of the equation 



x = - px, 

 with the conditions that when t = 0, x = a, x = 0, is x = a cos (t \//i). 



