100 



KINEMATICS. 



[186. 



AQ 



We thus have a simple geometrical construction for the 

 elements a, e of the resulting motion from the elements a lt e 1 

 and 2 , e 2 of the component motions. As the period is the 

 same for the two component motions, the points P l and P 2 

 describe their respective circles with equal angular velocity so 

 that the parallelogram OP^PP^ does not change its form in the 

 course of the motion. 



186. The construction given in the preceding article can be 

 described briefly by saying that two simple harmonic motions 

 of equal period in the same line are compounded by geometrically 

 adding their amplitudes, it being understood that the phase- 

 angles determine the directions in which the amplitudes are to 

 be drawn. 



It follows at once that not only two, but any number of simple 

 harmonic motions, of equal period in the same line, can be com- 

 pounded by geometric addition 

 of their amplitudes into a sin- 

 gle simple harmonic motion in 

 the same line and of the same 

 period. 



Conversely, any given sim- 

 ple harmonic motion can be 

 F resolved into two or more 

 components in the same line 

 and of the same period. 



187. The kinematical mean- 

 ing of this composition of sim- 

 ple harmonic motions of equal 

 period in the same line will 

 perhaps be best understood 

 from the mechanism sketched 

 in Fig. 48. A cord runs from 



the fixed point A over the movable pulleys B, D and the fixed 

 pulleys C, E, and ends in F. Each of the movable pulleys 



Fig. 48. 



