The natural frequencies of the system are the two values of w where the denominator is equal to
zero. In the old days, we would have factored this equation into the form aw4+bw2+c=0, then
found the two roots using the quadratic equation a
w = - ± 2 - . Now it’s much
more convenient to put equation 12 into a spreadsheet and calculate the transmissibility over a
range of frequencies, as in Figure 9. There are now two natural frequencies, and two frequencies
at which the system can resonate. The slope above the second resonance is now –40 dB/decade