SHM Maximum Acceleration

Acceleration in simple harmonic motion peaks at the turning points, where displacement — and therefore the restoring force — is greatest: $a_{\text{max}} = A\omega^2$. The squared frequency is what makes high-frequency vibration so destructive. A 10 cm amplitude at 10 rad/s gives 10 m/s², about 1 g; keep the amplitude and raise ω to 100 rad/s and you get 1000 m/s², over 100 g.

This is why vibration specifications for electronics, aircraft components and shipping crates are quoted in g's over a frequency band rather than in millimetres of travel, and why a 5 cm amplitude shaker table running at about 19.8 rad/s already delivers 2 g. Loudspeaker cones face the same limit: at 20 kHz the excursion must fall to microns or the cone would tear itself apart. Note that $a_{\text{max}} = \omega \cdot v_{\text{max}}$, so the three SHM peak quantities chain together through a single factor of ω each time you differentiate.