and where ω2
1 = k/m and ω2
2 = 3k/m. The maximum values of C1 and C2 given bythese equations are infinitely large when ω = ω
1 and ω = ω2, respectively, so that
the amplitudes of oscillation would become infinite if the system were driven at one of its normal frequencies. (We had a similar situation when considering a driven oscillator in Section 3.2.1.) This is, of course, because we have neglected damping that would limit their values in real situations. Nevertheless we can conclude that a coupled oscillator will oscillate with large amplitude when it is driven at either of its normal frequencies. At other driving frequencies the masses will oscillate at the driving frequency but with much smaller amplitude. From Equation (4.35) we have