Position of a damped spring at time t, in seconds.
Solved in closed form rather than integrated step by step, which is what makes it usable from a
page builder: any page can be evaluated on its own, in any order, and asking twice gives the same
answer. A stepwise simulation would need every earlier frame first.
The three regimes are genuinely different solutions of the same equation, not a single formula
with edge cases — underdamped motion oscillates, critically damped is the fastest approach that
does not, and overdamped crawls in without ever crossing.
Position of a damped spring at time
t, in seconds.Solved in closed form rather than integrated step by step, which is what makes it usable from a page builder: any page can be evaluated on its own, in any order, and asking twice gives the same answer. A stepwise simulation would need every earlier frame first.
The three regimes are genuinely different solutions of the same equation, not a single formula with edge cases — underdamped motion oscillates, critically damped is the fastest approach that does not, and overdamped crawls in without ever crossing.