THE HUMAN MOTOR 



Another familiar and important kind of motion is that ex- 

 hibited by a pendulum or the piston of a steam engine or a tuning 

 fork. It is called Harmonic Motion. In fig. 2 let OM represent 

 a pendulum, the point of suspension being at O and the " bob " 

 at M. If the pendulum swings to the position M, the distance 

 M^ = s, and is called the displacement. 



A complete oscillation or cycle is performed when the pendulum 

 has swung to an equal distance in the 

 opposite direction to M 2 and has returned 

 to the starting point at M. The time 

 taken for the complete cycle is known as 

 the period denoted " T." The frequency 

 is the number of such cycles per second 

 denoted " N." 



In fig. 3 we see that the displacement 

 s = OMj X sin MOM!. Denote the length 

 of the pendulum, which is the radius of the arc of the circle 

 described thereby as " a." We have then : 



s = a sin MOMj (fig. 3). 



Taking to. as the angular speed of the oscillating point, the 

 angle MOM! will be equal to to/ at the end of the time t. 

 Then : s = a sin to/. 



Assume the circle in fig. 4 to have unit radius, then the sine of 

 an angle MOMj is the perpendicular M^, its cosine is Od ; and we 

 see that the sine takes values from O to 1, as the angle varies 

 from zero to 90, the cosine varies inversely. 

 The tangent of the angle MOM X is represented 

 by the perpendicular TM on OM, which cuts 

 radius OM, prolonged if necessary. The ampli- 

 tude of the oscillations, as shown by the angle 

 MjOMg, vide fig. 3, or the demi-amplitude <*t 

 will be zero, for to/ = zero, sin CD* = o, and the 

 amplitude will be zero. 



For co/ = 90 or -~ we have sin <*t = 1 ; 

 therefore s=a. It is to be noticed that at the end of the period, 

 T, the moving body has come back to its original position, having 



x 



\ / 



Fio. 4. 



traversed 360 or 



; therefore <o/ = 2 IT, or t= 



<o 



o_ 



the duration 



of / is thus equal to T ; therefore T= There are also N 



CO 



double oscillations or N periods per second ; thus N x T = 

 1, or N = = o~ ' ora S ain = "Y ' These sim ple calculations 



