Motion of a ball and bowl system:

Q.3.  Explain the motion of a ball in a bowl. Show that it is simple harmonic motion.

Ans.      Motion of a ball and bowl system:

Consider a ball is placed at the bottom of a bowl O, 'at equilibrium' position as shown in figure. When the ball is at the bottom of the bowl its weight mg is equal to the reaction R so net force is zero


When a ball is gently displaced from the center of a bowl it start oscillation about the center due to force of gravity which act as a restoring force.








Once the ball is place at the position A and then released, It will accelerate towards the mean position under its weight. At the mean piston it again maximum velocity and momentum so its moves up-to the position B due to inertia. At B it has zero velocity so zero kinetic energy but maximum potential energy.

Again from point B it will move towards O under the restoring Force having maximum velocity at O but does not stop at O due to inertia and will go up to A. In this way the ball will continue to oscillate between the points A and B about the point O, it has simple harmonic motion.