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Thus, we see that K is analogous to 1/C , which makes sense, because with a given current for a given time, a smaller capacitor will build up more voltage, whereas with a given velocity for a given time, a smaller spring will build up less force.

I don't understand why smaller spring will build up less force? I know that [itex]F = K\int vdt[/itex] and if [itex]v[/itex] is the same so [itex]x[/itex] is the same, and as [itex]K[/itex] is the same, so force is the same.