14.4 Simple Harmonic Motion and Uniform Circular Motion
In order to get an insight into simple S.H.M, we will co-relate it with uniform circular motion which we have already studied. The different parameters such as displacement, velocity, acceleration and time period of simple harmonic motion (S.H.M) can be understood by relating it with uniform circular motion. It has been observed that when a particle moves in a circular path, its projection on diameter of the circle executes S.H.M.
To study the simple harmonic motion, consider a turntable of radius with a ball attached to its rim. A beam of light casts a shadow of the ball on the screen (Fig 14.4). When the turntable rotates with constant angular speed , then the ball also moves along with it uniform circular motion. Its shadow on the screen oscillates executing to and fro motion across the screen in the form of simple harmonic motion, like a body attached to a spring.
(Fig. 14.4: The oscillation of the shadow of ball on screen. The ball is attached with uniformly rotating turn table.)