SHM Maximum Velocity
Worked example: 2 cm amplitude at 50 rad/s → 1 m/s — press Try an example to run it live, then adjust anything.
Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Try different units for next level excitement!
SHM Maximum Velocity explained
An oscillator is fastest as it whips through the centre, where all its energy is kinetic, and that peak speed is simply amplitude times angular frequency: . A mass swinging 2 cm either side at ω = 50 rad/s tops out at 0.02 × 50 = 1 m/s. Double the frequency and the peak speed doubles even though the mass covers the same ground — it just covers it in half the time.
Engineers use this constantly for vibration limits: a machine part vibrating at 300 rpm (ω ≈ 31.4 rad/s) with a 4 in amplitude is moving at about 3.2 m/s at mid-stroke, which sets bearing and seal requirements. The trap is unit-mixing — ω must be in radians per second, not hertz or rpm, so convert first (ω = 2πf) or the answer will be off by 2π or by 60.
SHM Maximum Velocity formula
- = Maximum velocity (m/s)
- = Amplitude (m)
- = Angular frequency (rad/s)
Missing one of these? Work it out first, then come back
- Maximum velocity — Linear Momentum (p = mv), Power from Force and Velocity (P = Fv)
- Amplitude — SHM Displacement at Time t, SHM Maximum Acceleration
- Angular frequency — SHM Displacement at Time t, SHM Maximum Acceleration