### Examples Of Simple Harmonic Motion

# Concepts to remember for Simple Harmonic Motion (SHM) for JEE and CBSE board exams:

## Definition of Simple Harmonic Motion (SHM)

- SHM is a periodic motion in which the restoring force is directly proportional to the negative displacement from the mean position.

## Conditions for SHM

- The force acting on the oscillating body must be directly proportional to the negative displacement from the mean position.
- The oscillating body must have a fixed equilibrium position.
- The oscillating body must not experience any damping forces.

## Properties of SHM:

- SHM is periodic motion.
- The motion repeats itself at regular intervals.
- The displacement from the mean position is sinusoidal.
- The acceleration is directly proportional to the displacement and opposite in direction.

## Examples of SHM:

- Motion of a mass-spring system
- Motion of a pendulum
- Circular motion with constant angular velocity
- Transverse waves on a string
- Longitudinal waves in a spring

## Equations of SHM:

- Displacement equation: $$x = A \cos(\omega t + \phi)$$
- Velocity equation: $$v = -A \omega \sin(\omega t + \phi)$$
- Acceleration equation: $$a = -A \omega^2 \cos(\omega t + \phi)$$
- Where A is the amplitude, ω is the angular frequency, and φ is the phase angle