714 



Elastic String vibrating in a Viscous Media* 



' system having only one degree of freedom, is then, for 

 its fundamental vibration, given by 



ZTTT 



dt 



2 9 



7T I 



? = 0, 



or 



Mg + B* + =?,,-o: 



Its period will be given by 

 T = 



V: 



R 5 



M/ 47r 2 iVl 2 

 If R is small compared with M, this reduces to 



T 



a /M/ 



Writing M = mZ, where m is the mass of unit length y 



we have 



i-V? 



which is the well-known formula for the period of an 

 undamped string. 



The motion of the middle point of the string will be 

 given by 



E 



9 = 9 m e 2M c 



2tt 

 T 



where g is its maximum displacement. 



2M 

 The relaxation -time is equal to -^-. 



The string uill cease to vibrate when 



R 



« /Mr 9 ,— 



This is the critical f Actional resistance which will make its 

 motion non-oscillatory. That the motion can be made non- 

 oscillatory can easily be shown by immersing a string made 

 of indiarubber, which vibrates freely in air, in glycerine. 

 In such a viscous medium, when displaced from its position 

 of equilibrium and then released, it no longer oscillates about 

 this position, but simply returns to it. 

 University of Cincinnati, 

 January 1911. 



