Past exam of the physics A course of the University of Cambridge / 2015 / Paper 2 / Section B / B6 / a / Solution

For $b^2>4mk$, define $\beta =\sqrt{{\gamma }^2-{\omega }_0^2}$. The two characteristic roots are real and negative:This is overdamping: there is no repeated oscillation, and the slow root controls late-time return. A generic initial velocity can still cause a single crossing of equilibrium, so “nonoscillatory” need not mean monotone for all initial data. For large $b$, the slow root approaches $-k/b$.