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Simple Harmonic Motion and Uniform Circular Motion

Consider a particle P moving along the circumference of a circle of radius 'a' with a uniform angular velocity ω. Q is the foot of the perpendicular drawn from P to the diameter YOY'. Q is called the projection of P on the diameter. As the particle moves along the circumference, Q moves to and fro along the diameter about the centre O. The motion of Q about O is said to be simple harmonic. O is called the mean position or equilibrium position. The time taken by Q for moving from Y to Y' and back to Y is called the time period T and it is equal to the period of rotation of the particle P.


SHM is also defined as projection of uniform circular motion upon a diameter of a circle. This circle is called the circle of reference and Q is called the vibrating particle.

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