= Solution
For $b^2>4mk$, define $\beta=\sqrt{\gamma^2-\omega_0^2}$. The two <characteristic roots> are real and negative:
$$
\boxed{x(t)=C_+e^{(-\gamma+\beta)t}+C_-e^{(-\gamma-\beta)t}.}
$$
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 $-k/b$.
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