Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the x-projection of the radius vector of the rotating particle P is [NCERT Exemplar]

Let angular velocity of the particle executing circular motion is ω and when it is at Q, it makes an angle θ as shownin the diagram.Clearly, θ =ωtNow, we can write OR              =OQ cos (90°-θ)              =OQ sin θ = OQ sin ωt               =r sin ωt                                                         (∵ OQ = r)⇒        x = r sin ωt = B sin ωt                                          (∵ r=B)                =B sin2πTt=B sin2π30tClearly, this equation represents SHM.