Simple Harmonic Motion And Uniform Circular Motion - Practice Questions & MCQ

Simple harmonic can be represented as a projection of circular motion.

If P moves uniformly on a circle as shown in the below figure, then its projection P′ on a diameter of the circle executes SHM.

As the particle P moves on the circle, The position of P′ on the x-axis is given by

x(t) = A cos (ωt + φ)

This is the equation of SHM on the x-axis with amplitude A and angular frequency as 

Where A is the radius of the circle

and   is the angle that the radius OP makes with the x-axis at t=0

Similarly, The position of P′ on the y-axis is given by

y(t)=  A sin (ωt + φ)

This also an SHM of the same amplitude as that of the projection on the x-axis, but differing by a phase of π/2.