A compression spring has a surge frequency of its own, ½·√(k/m) with its full active mass. Work it above about a thirteenth of that and the coils stop moving together, pass a wave along the spring instead, and clash.
A spring is not a massless stiffness — it is a distributed elastic mass, so it has longitudinal modes like any bar fixed at both ends. Below resonance the coils move as one. Near it they cannot settle between compressions, so a wave travels down the spring, coils collide, and the stress goes far above anything the static calculation shows. It is why valve springs fail at a particular rpm rather than gradually, and why the fix is stiffer wire or fewer coils rather than more material.
Only for repeated cycling. A spring compressed slowly, or once, never sees it — a suspension spring at a few hertz has margin to spare. Dual springs and progressive pitch deliberately break up the resonance, so a single-frequency check understates what a properly designed valve train can do.
Estimate with the rule, then check it against the calculator that models it properly.
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