BRIGHTMAP AI — SIMPLE HARMONIC MOTION

A point moves counterclockwise on a circle of radius A at constant angular speed omega.
Its projection onto a horizontal diameter has displacement x = A cos(omega*t + phi).
Velocity v = -A*omega*sin(omega*t + phi).
Acceleration a = -omega^2*x: proportional to displacement and towards equilibrium.
Period T = 2*pi/omega. Frequency f = omega/(2*pi).

Units: A and x in metres, t in seconds, omega in radians per second, phi in radians.
At equilibrium: maximum speed A*omega; zero acceleration.
At the extremes: zero velocity; maximum acceleration magnitude A*omega^2.
Changing amplitude does not change period at fixed angular frequency.
The shadow's speed changes even though the rotating point's speed is constant.

Explore: https://www.brightmapai.pk/discover/physics/shm-circular-motion