I2 5 .] 



RECTILINEAR MOTION. 



63. 



123. The motion represented by equations (21) and (22) 

 belongs to the important class of simple harmonic motions (see 

 Arts. 177 sq.). The particle reaches the centre when s = o, i.e. 

 when /^=?r/2, or at the time /=7r/2/i,. At this time the 

 velocity has its maximum value. After passing through the 

 centre the point moves on to the other end, P v of the diameter, 

 reaches this point when s= R, i.e. when yu,/=7r, or at the time 

 t=TT/fj,. As the velocity then vanishes, the moving point 

 begins the same motion in the opposite sense. 



The time of performing one complete oscillation (back and 

 forth) is called the period of the simple harmonic motion ; it is. 

 evidently 



. T= 4 --=-- 



2JJ, p 



124. Exercises. 



(1) Equation (19) is a differential equation whose general integral 

 is known to be of the form 



s = Ci sin//,/ + C 2 cos/x/; 



determine the constants C l} C 2 and deduce equations (21) and (22). 



(2) Find the velocity at the centre and the period, taking ^=32 

 and R = 4000 miles. 



(3) If the acceleration, instead of being directed toward the centre, 

 is directed away from it, the equation of motion would ^d^s/dt^^s . 

 Investigate this motion, which can be imagined as produced by a force 

 of repulsion emanating from the centre. 



125. Retardation Due to a Resisting Medium. We know from 

 observation that the velocity of a body moving in a liquid or gas 

 is continually diminished. The resistance of such a medium 

 may be regarded as a force producing a retardation, or negative 

 acceleration. The same may be said of the effect of friction. 

 *\ The law according to which such resistances retard the motion 

 must of course be determined by experiment. 



