Q. Explain simple harmonic motion by ball and bowl system.

Ball and Bowl System:

Let us examine that the motion of a ball placed in a bowl executes simple harmonic motion. When the ball is placed at the mean position 'O' as shown in figure (at the center of the bowl). In this position, the net force acting on the ball is zero. Hence there is no motion. Now, if we displace the ball to an extreme position 'A' and then release it, the ball starts moving towards the mean position 'O' due to the restoring force caused by its weight component. At position 'O' the ball gets maximum speed and due to inertia, it moves towards opposite extreme position 'B' with the restoring force that acts towards the mean position, the speed of the ball starts to decrease. The ball stops for a while at 'B' and then again moves towards the mean position 'O'. This ball's to and fro motion continues about the mean position 'O'. This result shows that the acceleration of the ball is directed towards `O'. Hence, the ball's to and fro motion about a mean position placed in a bowl is also an example of simple harmonic motion.