The Relation between Displacement and Time for a body moving with s.h.m.

Point p oscillates between points A and B with s.h.m. O is the equilibrium position. The displacement of p from the equilibrium position is x.

Consider the auxiliary circular motion. The radius of the circle is r.

	If, at t = 0, point p was at O, then
	Therefore

The velocity of point p at any instant must be equal to the component of the velocity of p’ in a direction parallel to A-B.

The magnitude of the velocity of point p’ is r. Therefore the magnitude of the velocity of p is given by

so,

Therefore, the maximum velocity of p is r and this occurs when p is at the equilibrium position.

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