Solution
= Solution
For $b^2<4mk$, put $\omega_d=\sqrt{\omega_0^2-\gamma^2}$. Complex-conjugate roots give the real solution
$$
\boxed{x(t)=e^{-\gamma t}[C\cos(\omega_dt)+D\sin(\omega_dt)].}
$$
This is <underdamping>: oscillation at $\omega_d$ persists within a decaying exponential envelope. <damping> reduces the oscillation <frequency> below $\omega_0$. Constants in all three cases are determined by two <initial conditions>.