In one <normal mode>, all moving bobs share the same frequency and fixed amplitude ratios. A real mode vector allows their phases to be chosen equal or differing by $\pi$, according to the signs of its components. A component equal to zero means that bob remains at rest in that mode and has no oscillation phase to assign.

Solution

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

 Solution (source code)