60 



ANALOGIES 



4.7. Electrical, Mechanical and Acoustical Systems of Two Degrees of 

 Freedom. — The simple resonant system of one degree of freedom has been 

 considered in the preceding section. It is the purpose of this section to 

 consider the parallel electrical circuit and the mechanical and electrical 

 equivalents. 

 The Electrical System 



The relation of the currents in Fig. 4.3 are 



k = k + h 



The voltage across the capacitance is 



The voltage across the inductance and resistance in series is 



dh 



e = L—r -\- TeIz 



dt 



Since g = z, equation 4.50 may be written 



d- = Z-^s + rEqz 



4.48 



4.49 



4.50 



4.51 



M . 



i_X 



rxi-q ^ 



iP X 



Xa 



p M 0, 



ELECTRICAL MECHANICAL ACOUSTICAL 



Fig. 4.3. Electrical, mechanical and acoustical systems of two degrees of freedom. 



The Mechanical System 



The total displacement in the mechanical system of Fig. 4.3 is the sum 

 of the displacement of the mass m and the displacement of the com- 

 pliance Cm- 



xi = X2 + xz 4.52 



Differentiating equation 4.52 with respect to the time, the velocities are 



^1 = ^2 + xz 4.53 



The force applied to the spring is 



fM = ^ 4.54 



