Simple Harmonic MotionSt Peter's Science Portal · NCEA L3 Mechanics
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Mechanics · Simple Harmonic Motion

Simple Harmonic Motion

Both a swinging pendulum and a mass on a spring undergo SHM: the displacement, velocity and acceleration all follow sinusoids set by the angular frequency ω. Only ω differs — a pendulum has ω = √(g/L), a spring has ω = √(k/m). Use the Pendulum and Spring tabs to watch the motion and phasors, the Live solver to work any case by hand, and Quiz to test yourself.

Phasor circle

A phasor is a vector of length A rotating at angular frequency ω. Its projection onto the vertical axis traces the SHM value: the rotating arrow makes angle ωt, and the height of its tip is A·sin(ωt) (or A·cos(ωt), depending on where it starts). Pick which quantity to show and watch the trig build the value.

t = 0.00 s
The bob/block sits where the green projection line points.
y = 0.00 m
v = 0.00 m s⁻¹
a = 0.00 m s⁻²