Figure as given depicts circular motions. The radius of the circle, the period of revolution, the initial position and the sense of revolution are indicated in the figure. Obtain the simple harmonic motions of the x-projection of the radius vector of the rotating particle P in each case.

At t = 0, OP makes an angle of 45° = π/4 rad with the (positive direction of) x-axis. After time t, it covers an angle 2π/T t in the anticlockwise sense, and makes an angle of 2π/T t + π/4 with the x-axis.

The projection of OP on the x-axis at time t is given by, x (t) = Acos(2π/T t +π/4). For T = 4 s, x (t) = A cos 2π/T t + π/4 which is a SHM of amplitude A, period 4 s, and an initial phase π/4.