Simple Harmonic Motion

The general solution of equation (1) is x = a sin (ωt + δ)

Relationship between simple harmonic motion and circular motion

Simple harmonic motion is the projection of a uniform circular motion on a diameter.

Method to find the time taken, t, between two points in SHM :

1.   Draw a circle center at the equilibrium position with the amplitude of SHM as radius

2.   Draw a diameter through the two given points and find out its corresponding points on the circle.

3.   Calculate the angle θwhere θ= angle subtended at the center by these two points

4.   By formula   to calculate t.  ( T = period of SHM )

Examples of SHM :

mass-spring system : 

The simple pendulum :

Energy of simple harmonic motion

Simple Harmonic Motion :

The direction of the external force is always directed towards the equilibrium position and the magnitude of the external force is directly proportional to its distance from the equilibrium position..

Method to solve problems concerned with SHM

1.      Draw a free body diagram

2.      Find out the net force acting on the object in the direction 

        towards the fixed point

3.      Apply Newton’s second law equation to write down the equation

         of motion