= Solution
Here $x(t)$ is displacement from equilibrium, in metres; $m>0$ is the oscillating <mass>, in kilograms; $b\geq0$ is the coefficient of linear viscous <damping>, in $\mathrm{kg\,s^{-1}}$; and $k>0$ is the spring constant, in $\mathrm{N\,m^{-1}}$. The terms $m\ddot x$, $b\dot x$ and $kx$ are respectively the inertial term, the opposing velocity-dependent damping term and the opposing displacement-dependent restoring term when moved to the <force> side of <Newton's second law>.
$F_0$ is a possibly complex driving-force <complex amplitude>, measured in newtons. $\omega$ is the driving <angular frequency> in $\mathrm{rad\,s^{-1}}$, and taking the real part of $F_0e^{i\omega t}$ gives the physical sinusoidal <force>. Its <frequency> in hertz is $f=\omega/(2\pi)$. The natural undamped <angular frequency> and damping rate are
$$
\boxed{\omega_0=\sqrt{k/m},\qquad\gamma=b/(2m).}
$$
This <damped harmonic oscillator> model assumes a linear restoring <force> and a linear, instantaneous viscous damping law.
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