ONE DEGREE OF FREEDOM 57 



Assume that the frictional force/M, in dynes, acting upon the mass m as 

 it sHdes back and forth is proportional to the velocity as follows, 



Jm = TmX • 4.30 



where Vm = mechanical resistance, in mechanical ohms, and 

 X — velocity, in centimeters per second. 

 The rate at which mechanical energy, in ergs per second, is converted 

 into heat is 



Dm = Jm^ — fM^ 4.31 



The rate at which acoustical energy, in ergs per second, is radiated is 



Da = vaX^ 4.32 



where Va — acoustical radiation resistance, in acoustical ohms, and 

 X = volume current, in cubic centimeters per second. 



Acoustic radiation resistance will be considered in Sec. 5.7. 



D. Equations of Motion. -^ The rate at which work is done by the ap- 

 plied electromotive force is qE^'^^ = eq. The rate at which work is done 

 by the applied mechanical force is xF^'^^ = /mX. The rate at which work 

 is done by the applied acoustical pressure is XPe"^' = pX. 



The rate of decrease of energy {Tk + Vp) of the system plus the rate 

 at which work is done on the system by the external forces must equal the 

 rate of dissipation of energy. Writing this sentence mathematically yields 

 the equations of motion for the three systems. . 

 Electrical 



Lqq + r^f + |^ = Re'^^'q 4.33 



C 



E 



Mechanical 



Lq+rEq+^ = E^'^' 4.34 



XX 



mxx + rEX^ + 77- = ^^"'^ ^•'^^ 



mx + VeX + ^ = Fe^'"' 4.36 



