MCQ Practice – Oscillations | Academia Aeternum
Physics / Class XI / Chapter 13 – Oscillations / MCQ Practice
Multiple Choice Questions

50 MCQs on
Oscillations

A curated bank of 50 multiple-choice questions spanning NCERT fundamentals to JEE Advanced — with full topic coverage, difficulty progression, and previous year exam questions from IIT-JEE, NEET, BITSAT, KVPY, and more.

IIT-JEE NEET CBSE Board BITSAT / CUET KVPY / Olympiad
Start MCQ Practice View Analytics
50
Questions in this set
NCERT Basic (10)
NCERT Moderate (15)
JEE Entry (5)
JEE Moderate (8)
JEE Advanced (12)
6
Topic Clusters
8+
Exam Sources
30 min
Avg. Duration
Question Intelligence

Detailed MCQ Analytics — First 50 Questions

Difficulty Distribution

NCERT – Basic 10
NCERT – Moderate 15
JEE – Entry Level 5
JEE – Moderate 8
JEE – Advanced 12

Topic Share (Q1–50)

SHM Fundamentals36%
Energy (KE/PE)20%
Phase & Graphs16%
Spring & Pendulum16%
Kinematics (v,a,x)12%

Sub-Topic Frequency

Energy KE / PE / Total10
SHM Conditions & Force9
ω, T, f Relationships9
Displacement, v & a8
Phase & Phase Difference5
Pendulum Systems5
Spring-Mass System & k4

Question-Level Difficulty Heat Map — Q1 to Q50

NCERT Basic NCERT Moderate JEE Entry JEE Moderate JEE Advanced

Question Source Breakdown (Q1–50)

NCERT Textbook25
JEE / IIT-JEE Pattern25
Concept Analysis

Most Tested Concepts in This Set

Highest ⚡
10

Energy in SHM

KE, PE, total energy, energy at x=A/2, average energy over cycle — single most tested cluster in this set.

Very High 〰️
9

SHM Conditions & Force

F=−kx condition, restoring force, conservative nature — appears at every difficulty level from Q1 to Q50.

Very High 🔄
9

ω, T, f Relationships

Angular frequency, time period, frequency — their mutual relations and dependence on system parameters like m and k.

High 📐
8

Kinematics (v, a, x)

Velocity, acceleration, displacement — maxima, minima, and behaviour at mean vs. extreme positions.

Medium 🕰️
5

Pendulum Systems

T=2π√(L/g), effect of g, seconds pendulum, pendulum on Moon — exam favourites recurring across 25+ years of JEE/NEET.

Medium 🌀
4

Spring-Mass & k

T=2π√(m/k), dimension of spring constant, effect of doubling m or k — critical for JEE Moderate and above.

Learning Path

Difficulty Progression — Recommended Approach

10
NCERT Basic
Q 1 – 10
15
NCERT Moderate
Q 11 – 25
5
JEE Entry
Q 26 – 30
8
JEE Moderate
Q 31 – 38
12
JEE Advanced
Q 39 – 50
Quick Reference

Formulas You Will Need Most

Displacement
x = A sin(ωt + φ)
Velocity
v = ω√(A²−x²)
Acceleration
a = −ω²x
Total Energy
E = ½mω²A²
Spring Period
T = 2π√(m/k)
Pendulum Period
T = 2π√(L/g)
Angular Frequency
ω = 2π/T = 2πf
KE at position x
KE = ½mω²(A²−x²)
Solving Strategy

Smart Tips for This MCQ Set

🎯
Position-First Approach

For every v, a, or energy question — first identify whether the particle is at mean, extreme, or x=A/2. This resolves 80% of options instantly.

📊
Graph Shape Trap

a–x graph is a straight line with negative slope (not a curve). KE–x and PE–x are parabolas. These are frequently distorted in answer options.

⚡
Amplitude Doubling → Energy ×4

Since E = ½mω²A², doubling amplitude gives 4× energy, not 2×. This appears in Q7, Q11, and Q40 — three differently worded versions of the same rule.

🔄
Phase Relationship Chain

v leads x by π/2. a leads v by π/2. So a is π ahead of x — anti-phase. Three questions (Q14, Q32, Q44) directly test this chain.

🌙
Moon / Hill Pendulum

On Moon or a hill: g decreases → T increases → pendulum clock runs slow. Both give the same directional change — a deliberate trap in Q36.

🧮
KE = PE at x = A/√2

When kinetic energy equals potential energy, displacement is A/√2 ≈ 0.707A. Q13 (NCERT) and Q39 (JEE Advanced) frame the same result differently.

Ready to Attempt 50 Questions?

Attempt in order for best learning — or jump directly to a difficulty tier. Detailed solutions follow each section.

Begin from Q1 Review Analytics
🎯 Knowledge Check

Physics — OSCILLATIONS

50 Questions Class 11 MCQs
1
The motion of a particle executing simple harmonic motion is characterized by which of the following restoring forces? [NCERT – Basic]
2
The SI unit of angular frequency in simple harmonic motion is: [NCERT – Basic]
3
The time period of a simple harmonic oscillator depends on: [NCERT – Basic]
4
At the mean position of SHM, the acceleration of the particle is: [NCERT – Basic]
5
The phase of a particle in SHM is a measure of: [NCERT – Basic]
6
In SHM, the velocity of the particle is maximum at: [NCERT – Basic]
7
The total energy of a particle executing SHM is proportional to: [NCERT – Basic]
8
Which of the following quantities remains constant during SHM (ideal case)? [NCERT – Basic]
9
The displacement of a particle in SHM can be expressed as \(x = A\sin(\omega t)\). The maximum value of acceleration is: [NCERT – Basic]
10
The time period of a simple pendulum is independent of: [NCERT – Basic]
11
If the amplitude of SHM is doubled, the total energy becomes: [NCERT – Moderate]
12
The dimension of force constant \(k\) of a spring is: [NCERT – Moderate]
13
In SHM, when the kinetic energy equals the potential energy, the displacement is: [NCERT – Moderate]
14
The phase difference between velocity and displacement in SHM is: [NCERT – Moderate]
15
The graph between acceleration and displacement in SHM is: [NCERT – Moderate]
16
The effective length of a seconds pendulum on the surface of Earth is approximately: [NCERT – Moderate]
17
The angular frequency of a simple pendulum is given by: [NCERT – Moderate]
18
A particle executes SHM with amplitude \(A\). The ratio of maximum velocity to maximum acceleration is: [NCERT – Moderate]
19
The motion of a loaded spring in a vertical plane is SHM because: [NCERT – Moderate]
20
The time period of SHM is related to angular frequency by: [NCERT – Moderate]
21
A particle in SHM has zero velocity and maximum acceleration at: [NCERT – Moderate]
22
The energy of SHM is minimum at: [NCERT – Moderate]
23
If the length of a simple pendulum is increased four times, its time period becomes: [NCERT – Moderate]
24
The restoring force in SHM is conservative because: [NCERT – Moderate]
25
For SHM, which of the following is true? [NCERT – Moderate]
26
The equation \(x = A\cos(\omega t + \phi)\) represents SHM. The constant \(\phi\) is called: [JEE – Entry]
27
In SHM, the kinetic energy is maximum when the potential energy is: [JEE – Entry]
28
A mass \(m\) attached to a spring oscillates with angular frequency \(\omega\). If the mass is replaced by \(4m\), the new angular frequency is: [JEE – Entry]
29
The displacement of a particle executing SHM is zero at time \(t = 0\). Its equation of motion may be: [JEE – Entry]
30
In SHM, which quantity is always directed towards the mean position? [JEE – Entry]
31
The potential energy in SHM varies with displacement as: [JEE – Moderate]
32
If the phase of SHM is increased from \(\pi/6\) to \(\pi/3\), the phase difference is: [JEE – Moderate]
33
A particle executes SHM with frequency \(f\). The number of oscillations completed in time \(t\) is: [JEE – Moderate]
34
The acceleration of a particle executing SHM is proportional to: [JEE – Moderate]
35
In SHM, the time taken by the particle to go from mean position to extreme position is: [JEE – Moderate]
36
A simple pendulum is taken from Earth to Moon. Its time period will: [JEE – Moderate]
37
The total mechanical energy of SHM depends on: [JEE – Moderate]
38
In SHM, the work done by the restoring force over one complete cycle is: [JEE – Moderate]
39
The ratio of kinetic energy to potential energy at displacement \(x = A/2\) is: [JEE – Advanced]
40
A particle executes SHM with total energy \(E\). The kinetic energy at displacement \(x\) is: [JEE – Advanced]
41
In SHM, the average value of kinetic energy over one complete cycle is: [JEE – Advanced]
42
The maximum speed of a particle in SHM depends on: [JEE – Advanced]
43
A spring–mass system oscillates with time period \(T\). If both mass and spring constant are doubled, the new time period is: [JEE – Advanced]
44
The phase difference between acceleration and displacement in SHM is: [JEE – Advanced]
45
The displacement of a particle in SHM is given by \(x = A\sin(\omega t)\). The velocity is: [JEE – Advanced]
46
In SHM, which quantity is always zero at the extreme position? [JEE – Advanced]
47
The restoring force in SHM is maximum when the displacement is: [JEE – Advanced]
48
A body executes SHM. If its angular frequency is doubled, its time period becomes: [JEE – Advanced]
49
The motion of a particle is SHM if: [JEE – Advanced]
50
For a particle executing SHM, the ratio of maximum kinetic energy to maximum potential energy is: [JEE – Advanced]
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Frequently Asked Questions

Oscillatory motion is the motion in which a body moves repeatedly to and fro about a fixed mean position under the action of a restoring force.

Periodic motion is a type of motion that repeats itself after equal intervals of time, called the time period.

All oscillatory motions are periodic, but not all periodic motions are oscillatory because oscillatory motion must occur about a mean position.

SHM is a special type of oscillatory motion in which the restoring force is directly proportional to the displacement from the mean position and acts towards it.

A motion is SHM if the restoring force or acceleration is proportional to displacement and opposite in direction, i.e., \(a \propto -x\).

The mean position is the equilibrium position about which a body oscillates and where the net force acting on it is zero.

Amplitude is the maximum displacement of the oscillating body from its mean position.

Time period is the time taken by a body to complete one full oscillation.

Frequency is the number of oscillations completed per second and is the reciprocal of the time period.

Angular frequency \(\omega\) is defined as \(\omega = 2\pi f\), where \(f\) is the frequency of oscillation.

Phase represents the state of oscillation of a particle at a given instant, determined by the argument of the sine or cosine function.

Phase difference is the difference in phase angles of two oscillatory motions at the same instant.

The general equation of SHM is \(x = A\cos(\omega t + \phi)\), where \(A\) is amplitude and \(\phi\) is phase constant.

Restoring force is the force that always acts towards the mean position and tends to bring the body back to equilibrium.

SHM is called harmonic because its displacement varies sinusoidally with time.

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