igos.j KENNELLY AND UPSON— HUMMING TELEPHONE. 355 



w = 2TTn = yj A/m = y/a radians/sec. ( lo) 



where n is the frequency of the vibration in cycles per second. 



If, for example, the diaphragm of a telephone receiver had 

 simple elasticity and inertia without frictional retardation, such that 

 the elastic intensity a = 26.87 X 10'' dynes per cm. of displace- 

 ment and per gramme mass, then any displacement released would 

 be followed by an indefinitely sustained angular velocity 



w = V26.87 X 10® = 5,184 



radians per second, corresponding to ^^^825 cycles per second. If 

 the initial displacement were r = o.oi cm., the corresponding simple 

 circular orbit. Fig. 14, would have a radius of o.oi cm., an angular 

 velocity of 5,184 radians per second, an orbital velocity of 51.84 

 cm. per second, and an acceleration of 268,700 cm. per second. If 

 the elastic force A were 1.3435 X 10^ dynes per cm. of displace- 

 ment and the effective mass were 0.05 gm., the elastic force OF 

 would be 13,435 dynes, and the centrifugal force Of 13,435 dynes, 

 the two being equal and in complete opposition. 



Case of Free Vibration Damped and Unreinforced. Spiral 

 Orbital Motion. — In the case of the particle moving about a center, 

 let the motion be retarded by a force /', proportional to the velocity, 

 defined by the relation 



/' = — Tv^ — 27nyv dynes Z (11) 



Then the orbital displacement at any time t becomes 



The orbital velocity is 



v = i = r( — y + yw)€^-7+^'«^* cms./sec. Z (13) 



The orbital acceleration is 



c = v = $ = r( — y + ;w)-€(-7+^''^>* cms./sec.2 z (14) 



