Periodic and Oscillatory Motions:

Periodic Motion:

Periodic motion is the motion that reaches the same position after an equal interval of time. That is it repeats the motion along the same path having a fixed time interval.

Examples:

1) Revolution of the planets around the Sun,

2) The motion of the wheel of the car, and

3) The motion of the hands of the clock.

These are examples of periodic motion.

Oscillatory Motion:

Oscillatory motion is the back and fro motion about a mean position.

Examples:

1) The motion of the pendulum,

2) The motion of the bouncing ball, and

3) The motion of the tuning fork undergoes vibration.

These are examples of oscillatory motion.

Conclusion:

The periodic motion either be oscillatory or be non-oscillatory. But an oscillatory motion is always a periodic motion.

For example, the revolution of the planets around the Sun is periodic but not oscillatory. The motion of the pendulum is either periodic or oscillatory.

All oscillatory motion can be periodic but all periodic motion cannot be oscillatory.

Simple Harmonic Motion:

Simple Harmonic Motion (SHM) is a special type of oscillatory periodic motion in which a particle undergoes displacement equally on both sides of the equilibrium point because of restoring force.

The restoring force is a kind of force which always directed towards the equilibrium point.

The equation of a simple harmonic motion is given by,

y = A sin(kx + ωt + ɸ),

where ω is the angular velocity, k is the wave vector, A is the amplitude and ɸ is the phase. The frequency of a simple harmonic motion is independent of the amplitude.

The characteristics of a simple harmonic motion:

The characteristics of a simple harmonic motion are,

1.) Simple Harmonic Motion is always periodic in nature. This is the characteristics of a periodic wave.

2.) The acceleration of the restoring force is directly proportional to the displacement of the wave. This is the characteristics of an oscillatory wave.

3.) The acceleration of the restoring force is directed towards the equilibrium point which is the mean position. This is the characteristics of an oscillatory wave.

4.) In simple harmonic motion, the total energy is conserved.

5.) The periodic functions like a sine wave or cosine wave (i.e., sinusoidal wave) can be used to represent the simple harmonic motion.