Q. Define Simple Harmonic Motion and explain simple harmonic Motion.

Simple Harmonic Motion (S.H.M):

Definition:

“To and fro motion of a body in which acceleration is directly proportional to displacement and always directed towards mean position is known as Simple Harmonic Motion.”

Examples:
* Body attached to a spring horizontally on an ideal smooth surface.
* Motion of a simple and compound pendulum.
* Motion of a swing.
* Motion of ball in a bowl,               

Mathematically:                                                                                                                

Consider the motion of mass ‘m’ in fig there is no force on the mass ‘m’ because spring suffers no extension. Now the spring is pulled to the right through a distance “x” the restoring force is applies by spring.

The work done in pulling the spring through a distance “x” is stored in the form of potential energy of the spring. In return the spring applies a force to restore its position and the mass ‘m’ moves to the left. Thus potential energy changes into kinetic energy. At its mean position, the mass ‘m’ has a maximum speed and because of inertia the mass moves to the left. The spring then compresses and the motion of the mass ‘m’ retards. At its extreme left position all the energy is potential. This process repeats and the energy of the spring oscillates between potential and kinetic energy.

            Let x be the displacement of the mass ‘m’ at any instant then.

         Where “k” is called spring constant or force constant.