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Develop SHM equations from the motion of a point moving in a circle at constant angular velocity.

A point p moves in a circle of radius R, at constant angular velocity w. The origin of an x axis is at the center of the circle. Represent as vectors, the location, the velocity and the acceleration of point p, then show the x direction projection of these three vectors to represent the location, the velocity and the acceleration of a point which executes Simple Harmonic Motion, SHM.
See ATTACHMENT1 for a diagram.

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SEE ATTACHMENT2 TO OBSERVE THE FOLLOWING;
Vectors R, Vp and ap, are the location, velocity and acceleration of point p moving on a circle at constant angular velocity w.
The x direction components of the motion of point p, are defined as the motion equations of a point executing Simple Harmonic Motion, SHM.
Note 1. Note that point p, ...

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