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