Reference Circle → Simple Harmonic Motion

Watch the projection of uniform circular motion on a diameter. The projected point executes SHM.

Angle, θ0°
Displacement, x/A1.00
Period, T2.00 s
Angular frequency, ω3.14 rad/s

Controls

1.00
The radius of the reference circle becomes the SHM amplitude.
0.50 Hz
Uniform rotation and the projected SHM have the same period.
0°
Phase determines where the rotating point starts.
Observe: The horizontal coordinate of the rotating point is exactly the SHM displacement.
θ = ωt + φ    and    x = A cos θ

Reference circle and projection

SHM axis θ equilibrium −A +A x
rotating point SHM projection angle θ

Displacement–time graph

+A 0 −A time
Predict before changing a control

Increase the frequency. What happens to the rotation speed and the SHM period?