Oscillations & Simple Harmonic Motion (SHM)

Stage 1 – Page 1 | Foundations of Oscillatory Motion

1. What is Oscillatory Motion?

Oscillatory motion is a type of motion in which a body moves to and fro repeatedly about a fixed position called the mean position.

The motion is characterized by:

Repetition
Definite time interval
Restoring tendency towards mean position

Important: Every oscillatory motion is periodic, but every periodic motion is not oscillatory.

2. Periodic vs Non-Periodic Motion

Periodic Motion: Motion that repeats itself after equal intervals of time.

Rotation of Earth
Vibration of tuning fork
Motion of pendulum (small angle)

Non-Periodic Motion: Motion that does not repeat at regular time intervals.

Random motion of gas molecules
Car moving in traffic

Exam Trap: Do not confuse repetitive motion with periodic motion.

3. Mean Position, Extreme Position & Restoring Force

Mean Position: The central equilibrium position where the net force on the particle is zero.

Extreme Positions: The farthest points reached on either side of the mean position.

Velocity = 0 at extreme positions
Acceleration = maximum at extreme positions

Restoring Force: The force that always acts towards the mean position.

Key Concept: Existence of restoring force is the heart of oscillatory motion.

4. Time Period, Frequency & Angular Frequency

Time Period (T): Time taken to complete one oscillation.

Frequency (f): Number of oscillations per second.

f = 1 / T

Angular Frequency (ω):

ω = 2πf = 2π / T

Unit of ω → rad/s
Independent of amplitude

5. Conditions for Simple Harmonic Motion (SHM)

A motion is said to be Simple Harmonic Motion if:

The restoring force is directly proportional to displacement
The restoring force always acts towards mean position

Mathematically:

F ∝ −x

F = −kx

Minus sign indicates direction opposite to displacement.

6. Examples of SHM

Mass attached to a spring
Simple pendulum (small angular displacement)
Oscillation of liquid column
Electrical LC circuit (advanced)

Exam Note: Pendulum shows SHM only for small angles (sinθ ≈ θ).

7. What SHM is NOT

Circular motion (only projection is SHM)
Large angle pendulum motion
Random vibration

8. Why SHM is Crucial for IIT/JEE

Graph-based questions
Energy exchange understanding
Links with waves & AC
Tests conceptual clarity

Student Mindset: If SHM feels confusing, your foundation is incomplete — not your intelligence.

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