Consider the speaker model developed in Example 6.7.1. The model, whose transfer function is given by equation (3) in that example, is third order and therefore we cannot obtain a useful expression for the characteristic roots. Sometimes inductance L and damping c are small enough to be ignored. If L = 0, the model becomes second order,
(a) Obtain the transfer function X(s)/V(s) for the case where L = c = 0, and obtain the expressions for the two roots,
(b) Compare the results with the third-order case where
m = 0.002 kg
k = 4 x 105 N/m
Kf = 16N/A
Kb = 13 V.s/m
R = 12Ω
L = 10-3 H
C = 0