Periodic Motion:

Periodic motion refers to a type of motion that repeats itself over a specific period of time. It follows a regular and predictable pattern and can be represented by a periodic function, such as a sine or cosine wave. Some common examples of periodic motion include the swinging of a pendulum, the motion of a vibrating string, or the rotation of the Earth around the Sun.

Oscillatory Motion:

Oscillatory motion, on the other hand, is a specific type of periodic motion characterized by the back and forth movement of an object around a stable equilibrium position. It is also repetitive in nature but does not necessarily follow a sinusoidal pattern. Instead, it can have various waveforms, such as triangular, square, or sawtooth waves. Examples of oscillatory motion include the motion of a mass-spring system, the movement of a simple harmonic oscillator, or the vibrations of a guitar string.

Differences between Periodic and Oscillatory Motion:
1. Definition:
- Periodic motion refers to any motion that repeats itself after a fixed time interval, following a predictable pattern.
- Oscillatory motion specifically refers to the back and forth movement of an object around a stable equilibrium position.

2. Waveform:
- Periodic motion can have any waveform as long as it repeats itself after a fixed time period.
- Oscillatory motion can also have various waveforms, but they typically exhibit a symmetrical back and forth pattern.

3. Equilibrium Position:
- In periodic motion, there may or may not be an equilibrium position. The motion can occur between two extreme points or within a specific range.
- Oscillatory motion always involves an equilibrium position around which the object oscillates.

4. Amplitude:
- The amplitude of periodic motion can vary and may not be constant throughout the motion.
- Oscillatory motion usually has a constant amplitude, representing the maximum displacement from the equilibrium position.

5. Examples:
- Examples of periodic motion include the rotation of the Earth around the Sun, the swinging of a pendulum, or the periodic tides.
- Examples of oscillatory motion include the vibrations of a guitar string, the motion of a simple harmonic oscillator, or the oscillations of a mass-spring system.

In summary, while both periodic and oscillatory motion involve repetitive patterns, oscillatory motion specifically refers to the back and forth movement around an equilibrium position, whereas periodic motion can have various characteristics and waveforms. Oscillatory motion is a subset of periodic motion.