It follows from Equations (4.38) and (4.39) that when the driving frequency ω is
near the first normal frequency ω1 =√k/m, we have|C1||C2|, andxa ≈ xb,
i.e. the two masses oscillate in phase. When the driving frequency ω is near the
second normal frequency ω2 =√3k/m, one similarly obtains xa ≈−xb, i.e. the
two masses oscillate in anti-phase.
Since a coupled system oscillates with large amplitude when driven at one of its normal frequencies this provides a way of determining these frequencies exper-imentally. A good example of this is provided by the vibrations of molecules that