What is Simple Harmonic Motion?


Simple Harmonic Motion

Definition:      “The type of motion in which the acceleration of a body is always directly proportional to the displacement of the body from mean position (Equilibrium position) and is always directed towards the mean position is called as simple harmonic motion (SHM)”.

A body executing simple harmonic motion is called Simple harmonic oscillator (SHO).

It is a special case of oscillatory motion.

Mathematically:          a ∝ –x

                                    a = – ω2x

        i.            Here, ω is the constant of proportionality.

      ii.            Negative sign shows that acceleration is directly proportional towards the mean position.

Examples:

  1.                      Motion of mass attached with an elastic spring.
  2.                      Motion of simple pendulum with small angular motion.
  3.                      Motion of the projection of a body in circular motion.
  4.                     The electrons in a wire carrying alternating current.
  5.                    The vibrating particles of the medium in a sound wave

 

Conditions for S.H.M.

  •         The system must have inertia.
  •         The system should have restoring force.
  •        The system should be frictionless.
  •        The acceleration of the system should be directly proportional to the displacement and is always directed towards mean position i.e a ∝ –x

 

Difference between Periodic and Simple Harmonic Motion

Periodic Motion

Simple Harmonic Motion 

      1)      The displacement of the object may or may not be in the direction to the restoring force.

      2)      The periodic motion may or may not be oscillatory.

      3)      Examples:

The motion of the hands of a clock, the motion of the wheels of a car, etc.

     1)      The displacement of the object is always in the opposite direction to the restoring force.


      2)     The simple harmonic motion is always oscillatory.

      3)      Examples:

The motion of a pendulum, motion of a spring, etc.