Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2015 / Paper 2 / 17 / f

The largest angular-frequency magnitude is ${\omega }_3=\sqrt{(2+\sqrt{2})k/m}$. With overall amplitude $A$, the corresponding displacements areThus the two outer masses move together, while the middle mass moves oppositely with $\sqrt{2}$ times their amplitude. All three have the same period $2\pi /{\omega }_3$.