Understanding Simple Harmonic Motion

What is Simple Harmonic Motion?
Simple Harmonic Motion can be defined as the motion of an object where its acceleration is directly proportional to its distance from a fixed point along a path. The acceleration is said to always be directed towards the fixed point. This fixed point is known as the equilibrium position; this is because it is where the object that is swinging freely would come to rest given that it has lost all its energy.

The diagram below shows a pendulum in simple harmonic motion:

Pendulum in S.H.M

Where:
P is the equilibrium position (where the body would come to rest)
PQ & PR gives the amplitude position which is the greatest displacement from equilibrium position.
X is the position from the equilibrium position.

When the object is swinging freely you’ll probably realize that it moves faster when passing through its equilibrium position P, this is because the body’s acceleration and velocity is greatest as it passes through the equilibrium position. Also the opposite happens as the body leaves the equilibrium position, the acceleration and velocity lessens as the body’s position, x, moves further away from the equilibrium position.

Formulas involved in simple harmonic motion:

S.H.M formulas

The diagram below shows a spring in simple harmonic motion:

Spring in S.H.M