  # Introduction to Simple Harmonic Motion

Physics

## definition

### Time-period from equation of SHM

Equation of SHM:
Angular frequency
Frequency
Time-period
Example:
Acceleration-displacement graph of a particle executing SHM is as shown in the figure. Find the time period of oscillation.
Solution:
In SHM

or

so, from graph

Time period

## definition

### Applications of SHM

Some applications of SHM are:
• Simple harmonic motion of a pendulum is used for the measurement of time.
• Tuning of the musical instrument is done with the vibrating tuning fork which executes simple harmonic motion.
• Wave is a consequence of simple harmonic motion. Study of waves is indirectly the study of simple harmonic motion.
• Molecules are in simple harmonic motion. This study is called vibration spectroscopy.

## definition

### Characteristics of SHM

1. A restoring force must act on the body.
2. Body must have acceleration in a direction opposite to the displacement and the acceleration must be directly proportional to displacement.
3. The system must have inertia (mass).
4. SHM is a type of oscillatory motion.
5. It is a particular case of preodic motion.
6. It can be represented by a simple sine or cosine function