SHM Maximum Acceleration

a_{\max} = A \omega^{2}

amax =

A =

ω =

Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!

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Acceleration in simple harmonic motion peaks at the turning points, where displacement — and therefore the restoring force — is greatest: a_max = Aω². 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_max = ω·v_max, so the three SHM peak quantities chain together through a single factor of ω each time you differentiate.

SHM Maximum Acceleration

a_{\max} = A \omega^{2}

Where

$a_{\max}$ = Maximum acceleration
$A$ = Amplitude
$\omega$ = Angular frequency

Missing one of these? Work it out first, then come back

Maximum acceleration — Newton's Second Law, Final Velocity (Uniform Acceleration)
Amplitude — SHM Displacement at Time t, SHM Maximum Velocity
Angular frequency — SHM Displacement at Time t, SHM Maximum Velocity

Part of this formula set

Simple harmonic motion

7 formulasDisplacement, maximum velocity and maximum acceleration in an oscillation, with the two periods and the restoring force that generate them.