particle on a circle on a diameter y = + A y = y = A -y +y +y Light From Distant Source (A) (B) Shadow On Block Screen Screen at t > at t= y = A sinθ =A sin t A sin ( t) -y θ θ Shadow y y = r sin θ x = r cos θ x - - - - Unit Oscillations a map (or a relationship) between uniform circular (or revolution) motion to vibratory motion. Conversely, any vibratory motion or revolution can be mapped to uniform circular motion. In other words, these two motions are similar in nature. Let us first project the position of a particle moving on a circle, on to its vertical diameter or on to a line parallel to vertical diameter as shown in Figure .
. Similarly, we can do it for horizontal axis or a line parallel to horizontal axis. The following figures explain the position of particle at different time : Figure . The location of a particle at each instant as projected on a vertical axis P P x- axis y- axis o P P x- axis y- axis o P P x- axis y- axis o P P x- axis y- axis o P P x- axis y- axis o P P x- axis y- axis o P P x- axis y- axis o P P x- axis y- axis o - - - - Unit Oscillations As a specific example, consider a spring mass system (or oscillation of pendulum) as shown in Figure .
. When the spring moves up and down (or pendulum moves to and fro), the motion of the mass or bob is mapped to points on the circular motion. Figure . Motion of spring mass (or simple pendulum) related to uniform circular motion Thus, if a particle undergoes uniform circular motion then the projection of the particle on the diameter