Past exam of the mathematical methods II course of the University of Oxford / 2017 / 9 / d

With zero initial velocities, choosing the initial displacement proportional to one eigenvector excites only its normal mode. Suitable ratios areThe overall scale must remain small compared with $l$. Release each configuration from rest; its subsequent vector is its initial displacement multiplied by $\cos {\omega }_{j}t$. The middle bob is stationary in the second mode, while it moves oppositely with twice either outer amplitude in the third.