and where ω2
1
= k/m and ω2
2
= 3k/m. The maximum values of C1 and C2 given by
these equations are infinitely large when ω = ω1 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