1. What is Oscillation?

A repetitive to-and-fro motion about a mean (or equilibrium) position is called oscillation.

Ex: Swinging pendulum, vibrating tuning fork, moving fan blades.

2. Important AAI ATC Focused Concepts

3. Simple Harmonic Motion (SHM)

Definition: A type of oscillatory motion where acceleration is directly proportional to displacement and directed towards the mean position.

\( F = -k x \)

GenZ Example

If you pull a spring and leave it — it bounces back and forth around its rest position.

PYQ Type: SHM definition MCQ

4. Time Period of Simple Pendulum

The time taken for one complete oscillation.

\( T = 2\pi \sqrt{\frac{L}{g}} \)

Where:

L: Length of string
g: Acceleration due to gravity

Unit: seconds (s)

GenZ Example

Longer pendulum → slower swing.

PYQ Type: Time period formula direct MCQ

5. Time Period of Spring-Mass System

The time period for a mass oscillating on a spring.

\( T = 2\pi \sqrt{\frac{m}{k}} \)

Where:

m: Mass
k: Spring constant

GenZ Example

Heavier weight on a spring → slower up-down motion.

PYQ Type: Conceptual theory MCQ

6. Angular Frequency (ω)

The rate of change of angular displacement.

\( \omega = 2\pi f = \frac{2\pi}{T} \)

Where:

f: Frequency (Hz)

GenZ Example

Fan rotating faster = higher angular frequency.

7. Displacement, Velocity & Acceleration Equations

Equations describing SHM motion.

Displacement: \( x = A \sin(\omega t + \phi) \)
Velocity: \( v = \omega \sqrt{A^2 - x^2} \)
Acceleration: \( a = -\omega^2 x \)

Where:

A: Amplitude
φ: Phase constant

GenZ Example

Max stretch or compression of a spring shows its amplitude.

PYQ Type: Formula or property theory MCQ

8. AAI ATC PYQ Analysis (2021–2023)

2021 Shift 2: Formula-based MCQ on pendulum time period

2022 Shift 1: SHM definition theory MCQ

2023 Feb Shift 1: Relation between time period and length in pendulum

9. Oscillation Formula Quick Revision Sheet

Formula	Meaning
\( F = -k x \)	SHM restoring force
\( T = 2\pi \sqrt{\frac{L}{g}} \)	Pendulum time period
\( T = 2\pi \sqrt{\frac{m}{k}} \)	Spring time period
\( \omega = \frac{2\pi}{T} \)	Angular frequency
\( x = A \sin(\omega t + \phi) \)	Displacement in SHM
\( v = \omega \sqrt{A^2 - x^2} \)	Velocity in SHM
\( a = -\omega^2 x \)	Acceleration in SHM

10. Quick Concept Recap

Concept	GenZ Example
SHM	Bouncing spring toy
Time period increases with length	Longer pendulum = slower swing
Angular frequency	Faster fan = higher angular frequency
Max displacement = amplitude	Max stretch or compression of a spring

11. Final AAI ATC Takeaway

Focus Areas:

1-2 questions per shift
Time period formulas
SHM restoring force relation
Angular frequency
Definition MCQs

12. 10-Question AAI ATC-Style MCQ Mock Test — Oscillations

Q1. What is the time period of a simple pendulum of length 1m? (Use g=9.8 m/s²)
a) 0.5 s
b) 1.99 s
c) 6.28 s
d) 0.33 s
Ans: b

Q2. The relation F = –k x represents:
a) Hooke’s Law
b) Newton’s 2nd Law
c) SHM restoring force
d) Centripetal force
Ans: c

Q3. Angular frequency is given by:
a) 2πf
b) 2f/π
c) 2πT
d) π/2T
Ans: a

Q4. The maximum displacement of an oscillating particle from its mean position is called:
a) Amplitude
b) Frequency
c) Phase
d) Time period
Ans: a

Q5. What happens to the time period if the length of a pendulum is increased?
a) Increases
b) Decreases
c) Remains constant
d) Doubles
Ans: a

Q6. In SHM, acceleration is maximum at:
a) Mean position
b) Maximum displacement
c) Half amplitude
d) None
Ans: b

Q7. Unit of angular frequency (ω) is:
a) m/s
b) rad/s
c) s
d) Hz
Ans: b

Q8. A mass m attached to a spring with constant k oscillates with time period:
a) 2π √(m/k)
b) 2π √(k/m)
c) 1/2π √(k/m)
d) 2πk/m
Ans: a

Q9. Which of these is dimensionally same as frequency?
a) Angular speed
b) Time period
c) Speed
d) Displacement
Ans: a

Q10. If amplitude doubles in SHM, maximum velocity becomes:
a) Same
b) Double
c) Four times
d) Half
Ans: b