SHM Maximum Velocity

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: v_max = Aω. 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.