Previous Year MCQs – Oscillations | Academia Aeternum
Physics / Class XI / Chapter 13 — Oscillations / Previous Year MCQs
Previous Year Questions

Oscillations
PYQ Master Set

Fifty multiple-choice questions drawn directly from 8 major competitive and board examinations spanning 25 years — IIT-JEE, NEET, CBSE, AIIMS, BITSAT, KVPY, and Olympiad. Every question is exam-tagged with its year of appearance.

1997
Earliest Year
25
Years Covered
2021
Latest Year
8
Exam Boards
IIT-JEE JEE Main JEE Advanced NEET CBSE Board AIIMS BITSAT KVPY Olympiad
Begin PYQ Practice View Analytics
50
Previous Year Questions

Sourced from 8 exam bodies across 25 years of actual competitive and board papers. Each carries exam name and year.

JEE / IIT
18
NEET
12
CBSE
9
BITSAT
5
KVPY
4
AIIMS
2
50
Questions
25
Years
18
JEE PYQs
35 min
Duration
Question Intelligence

Detailed Analytics — 50 Previous Year Questions

Questions per Exam Board

IIT-JEE / JEE Main / Adv.18
NEET12
CBSE Board9
BITSAT5
KVPY4
AIIMS2

Topic Distribution

SHM Conditions & Kinematics30%
Energy KE / PE / Total24%
T, ω, f Relationships18%
Pendulum & Spring16%
Phase, Graph & Units12%

Questions by Decade

1997 – 20018
2002 – 20067
2007 – 20119
2012 – 201613
2017 – 202113

25-Year Coverage Timeline — Every Exam & Year Present in This Set

199720012005 2009201320172021

Question Map — Q1 to Q50 · Colour = Exam Board

JEE / IIT-JEE NEET CBSE BITSAT KVPY AIIMS Olympiad
Source Profile

Exam Board Breakdown

IIT-JEE / JEE Main / Adv.
18
1997, 1998, 1999, 2001, 2002, 2003, 2004, 2005, 2013, 2014, 2015, 2016, 2017, 2018, 2019
NEET
12
2005, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021
CBSE Board
9
2006, 2008, 2009, 2010, 2011, 2012, 2014, 2015
BITSAT
5
2014, 2015, 2016, 2017, 2018
KVPY
4
2010, 2011, 2014, 2016
AIIMS
2
2010
Olympiad
2
2012, 2013
Pattern Analysis

Most Tested Concepts Across 25 Years

Most Tested 〰️
15

SHM Conditions & Kinematics

Velocity at position x, acceleration direction, zero-crossing timing, and the defining condition F=−kx. The #1 topic across all 8 exam boards.

Very High ⚡
12

Energy in SHM

Total energy, KE at displacement x, energy when amplitude doubles, average KE over a full cycle. Especially dominant in JEE and AIIMS questions.

Very High 🔄
9

T, ω, f Relationships

How time period and frequency change when mass, spring constant, or pendulum length is altered. Consistently tested since 1997.

High 🕰️
8

Pendulum & Spring Systems

Pendulum on Moon, on a hill, with doubled length. Spring constant doubling and mass replacement. Classic multi-step problems from JEE 2000–2017.

Medium 📊
6

Phase & Graph Questions

Phase difference between v and x (π/2), a and x (π). Graph shape identification for a–x, KE–x, PE–x. Favoured by NEET and CBSE boards.

Medium 🔢
5

Units, Dimensions & Definitions

SI unit of angular frequency, dimension of spring constant k, definition of initial phase. Recurring in CBSE and AIIMS from 2006–2015.

Board-Wise Intelligence

What Each Exam Repeatedly Tests

🏆
JEE Loves Energy Combinations

Of the 18 JEE questions, 7 involve energy — often paired with amplitude changes or position-specific substitution. The formula E=½mω²A² is the single most useful equation for this subset.

🌿
NEET Focuses on Pendulum & Definitions

NEET questions lean towards conceptual pendulum scenarios — Moon, hill, doubled length — and definitional clarity. NEET rarely demands deep calculus derivations.

📐
CBSE Tests Units & Graph Shapes

Nearly 4 of 9 CBSE questions cover unit identification, dimension, or graph-type discrimination — "unit of angular frequency", "shape of a–x graph" — steadily from 2006 to 2015.

⚙️
BITSAT Uses Substitution Traps

BITSAT questions are numerically clean but use parameter-swap traps — doubling mass, halving k, replacing springs. Answer choices are arranged to catch the common directional error.

🔁
Three Concepts Are Perennial Repeaters

Maximum velocity (v=ωA), phase difference between a and x (π), and pendulum on Moon have appeared across IIT-JEE, NEET, and CBSE in multiple years.

📅
Post-2013 Questions Are Scenario-Based

Questions from 2013 onwards embed formulas in physical scenarios — spring on incline, pendulum in accelerating lift — rather than asking formula recall directly. Seen especially in JEE Main post-2013.

Exam Quick Reference

Formulas Most Used in These PYQs

Max Velocity
v_max = ωA
IIT-JEE 1998 — directly asked; also tested in NEET 2005 framing
Velocity at x
v = ω√(A²−x²)
Most-used formula in this entire set — appears in JEE, NEET, KVPY
Acceleration
a = −ω²x
CBSE 2008, NEET 2015 — definitional form; zero at mean position
Total Energy
E = ½mω²A²
AIIMS 2010, NEET 2016 — amplitude-squared relation is the key trap
Pendulum Period
T = 2π√(L/g)
NEET 2005, NEET 2017 — Moon/hill variant appears across 6 questions
Phase · v leads x
Δφ(v,x) = π/2
JEE Main 2013, NEET 2018 — phase chain questions build on this
Spring Period
T = 2π√(m/k)
BITSAT 2014, Olympiad 2013 — parameter-swap trap questions
KE = PE at
x = A/√2
JEE Main 2014, KVPY 2016 — same result, different level of framing
Solving Strategy

How to Approach PYQ Practise

1

Attempt Under Exam Conditions

Set a 35-minute timer — that mirrors the per-section pace of JEE Main and NEET. Resist looking at the exam tag until after you have answered. Train your instinct, not your memory.

2

Read the Exam Tag After Each Answer

Once you answer, note which board set the question. Over time you will recognise the house style of each exam — JEE's layered framing vs NEET's direct phrasing vs CBSE's definition-first style.

3

Identify the Energy Trap Every Time

Energy questions are the most frequent here. Before solving, ask: is this asking about E, KE, or PE? Confirm whether the amplitude or position is given. E ∝ A² catches most wrong answers.

4

Review Pendulum Questions as a Cluster

After finishing, pull out all pendulum questions and revisit them together. The Moon, hill, elevator, and doubled-length variants are different faces of the same T = 2π√(L/g) logic and are best understood as a family.

50 Real Exam Questions Await

Each question is sourced from an actual competitive paper — exam-tagged, year-dated, and sequenced for maximum learning. Detailed solutions follow the question set.

Begin Practice Review Analytics
Score 0 / 50
⏱ 00:00
Q1
The displacement of a particle executing SHM is given by \(x = A\sin(\omega t)\). The maximum velocity of the particle is
(Exam: IIT-JEE Year: 1998)
(A) \(A\omega\)
(B) \(A/\omega\)
(C) \(\omega/A\)
(D) \(A^2\omega\)
Q2
The time period of a simple pendulum depends on
(Exam: NEET Year: 2005)
(A) mass of the bob
(B) amplitude of oscillation
(C) length of the pendulum
(D) material of the string
Q3
In SHM, acceleration is proportional to
(Exam: CBSE Year: 2008)
(A) velocity
(B) displacement
(C) square of displacement
(D) time
Q4
The total energy of a particle executing SHM is
(Exam: AIIMS Year: 2010)
(A) maximum at mean position
(B) minimum at extreme position
(C) constant throughout motion
(D) zero at mean position
Q5
The phase difference between displacement and velocity in SHM is
(Exam: JEE Main Year: 2013)
(A) \(0\)
(B) \(\pi/2\)
(C) \(\pi\)
(D) \(3\pi/2\)
Q6
For a mass-spring system, the angular frequency is
(Exam: BITSAT Year: 2014)
(A) \(\sqrt{mk}\)
(B) \(\sqrt{k/m}\)
(C) \(k/m\)
(D) \(m/k\)
Q7
At the extreme position of SHM, the kinetic energy is
(Exam: NEET Year: 2016)
(A) maximum
(B) minimum
(C) zero
(D) equal to potential energy
Q8
The restoring force in SHM always acts
(Exam: IIT-JEE Year: 2002)
(A) along velocity
(B) opposite to displacement
(C) perpendicular to motion
(D) along displacement
Q9
The time period of SHM is independent of
(Exam: KVPY Year: 2011)
(A) mass
(B) force constant
(C) amplitude
(D) system type
Q10
The unit of angular frequency is
(Exam: CBSE Year: 2006)
(A) Hz
(B) rad/s
(C) s
(D) m/s
Q11
If the length of a pendulum is doubled, its time period becomes
(Exam: NEET Year: 2017)
(A) half
(B) double
(C) \(\sqrt{2}\) times
(D) \(1/\sqrt{2}\) times
Q12
In SHM, the potential energy is maximum at
(Exam: JEE Main Year: 2014)
(A) mean position
(B) extreme positions
(C) midway
(D) everywhere same
Q13
The phase of SHM at \(t=0\) is called
(Exam: Olympiad Year: 2012)
(A) final phase
(B) angular frequency
(C) initial phase
(D) time period
Q14
The relation between linear frequency \(f\) and angular frequency \(\omega\) is
(Exam: CBSE Year: 2009)
(A) \(\omega = f\)
(B) \(\omega = 2\pi f\)
(C) \(f = 2\pi \omega\)
(D) \(f = \omega^2\)
Q15
The acceleration of a particle in SHM is zero at
(Exam: NEET Year: 2018)
(A) extreme position
(B) mean position
(C) midway
(D) everywhere
Q16
The time period of a mass-spring system increases if
(Exam: IIT-JEE Year: 2004)
(A) mass is increased
(B) spring constant is increased
(C) amplitude is increased
(D) gravity is increased
Q17
In SHM, velocity is maximum at
(Exam: BITSAT Year: 2015)
(A) extreme position
(B) mean position
(C) midway
(D) everywhere
Q18
The energy of SHM is proportional to
(Exam: KVPY Year: 2010)
(A) amplitude
(B) square of amplitude
(C) time period
(D) frequency
Q19
A particle executes SHM with period \(T\). The time taken to go from mean to extreme position is
(Exam: JEE Main Year: 2016)
(A) \(T/2\)
(B) \(T/4\)
(C) \(T/8\)
(D) \(T\)
Q20
The dimension of spring constant \(k\) is
(Exam: CBSE Year: 2011)
(A) \(MLT^{-2}\)
(B) \(MT^{-2}\)
(C) \(MT^{-1}\)
(D) \(ML^{-1}T^{-2}\)
Q21
The graph between displacement and time for SHM is
(Exam: NEET Year: 2019)
(A) straight line
(B) parabola
(C) sine curve
(D) hyperbola
Q22
The restoring force in SHM is conservative because
(Exam: IIT-JEE Year: 2001)
(A) it depends on velocity
(B) it depends on displacement
(C) work done is path dependent
(D) energy is not conserved
Q23
For small oscillations, the motion of a simple pendulum is SHM because
(Exam: NEET Year: 2014)
(A) angle is large
(B) \(\sin\theta \approx \theta\)
(C) string is heavy
(D) air resistance is present
Q24
The maximum acceleration in SHM is
(Exam: JEE Advanced Year: 2017)
(A) \(A\omega\)
(B) \(A\omega^2\)
(C) \(\omega/A\)
(D) \(A^2\omega\)
Q25
If the amplitude of SHM is doubled, the total energy becomes
(Exam: BITSAT Year: 2016)
(A) double
(B) half
(C) four times
(D) unchanged
Q26
The time period of SHM is minimum when
(Exam: Olympiad Year: 2013)
(A) mass is maximum
(B) force constant is maximum
(C) amplitude is maximum
(D) displacement is maximum
Q27
In SHM, velocity is zero at
(Exam: NEET Year: 2020)
(A) mean position
(B) extreme positions
(C) both mean and extreme
(D) everywhere
Q28
The phase difference between acceleration and displacement in SHM is
(Exam: IIT-JEE Year: 1999)
(A) \(0\)
(B) \(\pi/2\)
(C) \(\pi\)
(D) \(3\pi/2\)
Q29
The time period of a pendulum on the Moon is
(Exam: NEET Year: 2012)
(A) same as on Earth
(B) less than on Earth
(C) more than on Earth
(D) zero
Q30
The displacement in SHM is minimum at
(Exam: CBSE Year: 2010)
(A) mean position
(B) extreme positions
(C) midway
(D) everywhere
Q31
The velocity-time graph of SHM is
(Exam: JEE Main Year: 2015)
(A) linear
(B) parabolic
(C) sinusoidal
(D) circular
Q32
The restoring force constant of a spring is doubled. The new time period becomes
(Exam: BITSAT Year: 2017)
(A) \(T\)
(B) \(2T\)
(C) \(T/\sqrt{2}\)
(D) \(\sqrt{2}T\)
Q33
In SHM, the average kinetic energy over a cycle equals
(Exam: KVPY Year: 2014)
(A) zero
(B) total energy
(C) half of total energy
(D) twice the total energy
Q34
The condition for SHM is
(Exam: IIT-JEE Year: 2003)
(A) force proportional to velocity
(B) force proportional to displacement
(C) force independent of displacement
(D) force proportional to time
Q35
The frequency of SHM is
(Exam: NEET Year: 2011)
(A) inverse of period
(B) equal to period
(C) square of period
(D) twice the period
Q36
The kinetic energy of SHM is maximum when
(Exam: JEE Advanced Year: 2018)
(A) displacement is zero
(B) displacement is maximum
(C) acceleration is maximum
(D) force is maximum
Q37
A body executes SHM with angular frequency \(\omega\). Its frequency is
(Exam: CBSE Year: 2012)
(A) \(\omega\)
(B) \(\omega/2\pi\)
(C) \(2\pi\omega\)
(D) \(\omega^2\)
Q38
The motion is SHM if acceleration is
(Exam: NEET Year: 2015)
(A) constant
(B) proportional to velocity
(C) proportional to displacement
(D) proportional to square of displacement
Q39
The time period of SHM depends on
(Exam: IIT-JEE Year: 2000)
(A) amplitude
(B) initial phase
(C) system parameters
(D) displacement
Q40
In SHM, the restoring force is zero at
(Exam: NEET Year: 2013)
(A) extreme position
(B) mean position
(C) midway
(D) everywhere
Q41
The total energy of SHM is proportional to
(Exam: BITSAT Year: 2018)
(A) amplitude
(B) square of amplitude
(C) frequency
(D) time period
Q42
The acceleration in SHM is maximum at
(Exam: CBSE Year: 2014)
(A) mean position
(B) extreme positions
(C) midway
(D) everywhere
Q43
A pendulum clock runs slow on a hill because
(Exam: NEET Year: 2010)
(A) mass increases
(B) gravity decreases
(C) length increases
(D) air density decreases
Q44
The equation of SHM is
(Exam: IIT-JEE Year: 1997)
(A) \(x = A\sin(\omega t)\)
(B) \(x = vt\)
(C) \(x = at^2\)
(D) \(x = kt\)
Q45
The restoring force constant has SI unit
(Exam: CBSE Year: 2015)
(A) N
(B) N/m
(C) J
(D) kg
Q46
The motion of a particle is SHM if
(Exam: JEE Main Year: 2017)
(A) velocity is constant
(B) force is constant
(C) acceleration is proportional to displacement
(D) displacement is constant
Q47
The energy of SHM is equally divided between kinetic and potential energy at
(Exam: KVPY Year: 2016)
(A) extreme position
(B) mean position
(C) midway between mean and extreme
(D) everywhere
Q48
The time period of SHM increases if
(Exam: NEET Year: 2021)
(A) mass increases
(B) force constant increases
(C) amplitude increases
(D) displacement increases
Q49
In SHM, the direction of acceleration is always
(Exam: IIT-JEE Year: 2005)
(A) along velocity
(B) along displacement
(C) opposite to displacement
(D) perpendicular to velocity
Q50
The maximum potential energy of SHM is
(Exam: JEE Advanced Year: 2019)
(A) zero
(B) equal to total energy
(C) half of total energy
(D) twice the total energy

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