Root of a nonlinear equation, as the last step of an ODE solution

What better use for a computer algebra system than a problem whose solution you know intuitively, and for which the paper-and-pencil work feels too daunting to start?  Here’s a problem that exploits what we know about the solutions of damped driven oscillators, making use of the usual ODE capabilities in Maxima, together with a nonlinear solve with find-root at the end.

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