Consider the Moon at a distance A from the center of the Earth, rotating in a circular motion with a constant angular velocity. Let the Earth's center be the origin of the displacement-time coordinate system. When the Moon moves to a position P, its projection P' on the x-axis makes an angle Ф. As the Moon moves further around the Earth at any time t, it makes an angle ωt+Ф. Based on the Moon's projection on the x or y-axis, the position of the projection can be denoted by either a cosine or sine function. The period of the Moon can be given by the circumference of the Earth's orbit over its velocity. Recalling the velocity equation from energy conservation and modifying it, the period of the Moon's projection is determined. The velocity of the Moon acts tangentially, while the acceleration of the Moon is directed radially inward. The x-component of the velocity and acceleration of the Moon is equal to the velocity and acceleration of the Moon's projection. Their magnitudes are obtained by recalling the velocity and acceleration equations. As observed, the time period, position, velocity, and acceleration equations of the Moon's projection are similar to that of a simple harmonic oscillator. Therefore, the projection of a uniform circular motion along the diameter of a circle on which the circular motion occurs represents simple harmonic motion.