JEE Main · Physics · Oscillations
SHM Equations: JEE Main previous year questions
57 questions in the 108 JEE Main shifts Lumi analysed, in 7 of 8 years. Pattern: Asked most years. 15 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 57
- in 48 of 108 shifts
- Years asked
- 7/8
- last asked 2026
- Weighted estimate
- 0.4
- model; history: 0.4 a shift on average, typically 0.2–0.6
Key findings
- 01
Asked in 7 of 8 years with analysed shifts and in 48 of 108 shifts: 57 questions, #45 of 196 topics.
- 02
54% of its questions since 2020 tested an idea no earlier year had asked; 13 repeated an idea from the year before.
- 03
The most repeated idea is Velocity and Accel vs Position, asked 6 times in 6 shifts (2021, 2022, 2024, 2026), most often as “time period from v squared relation”.
- 04
JEE Main has asked 21 of the 59 ideas in this topic; 32 have never been asked, directly or inside another question.
- 05
Mostly asked as single correct (47%); 37% need a numerical answer, 53% are easy and 5% hard.
- 06
The skill tested most is calculation (44%), then application (25%).
Questions a shift, year by year
Out of the 25 Physics questions in a shift. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift.
Raw count: 2017: 0 in 1 shift · 2020: 2 in 12 shifts · 2021: 23 in 24 shifts · 2022: 11 in 24 shifts · 2023: 6 in 12 shifts · 2024: 7 in 18 shifts · 2025: 3 in 8 shifts · 2026: 5 in 9 shifts.
- Up to 2023
- 0.3
- a shift, of 25
- Since 2024
- 0.4
- 0.1
- Usual gap
- 1.0 yrs
- between years asking it
- Shifts with it
- 48/108
- 44% of analysed shifts
Revise first
- Velocity and Accel vs Position · asked 2021, 2022, 2024, 2026
- SHM Definition and Force Law · asked 2021, 2023, 2024, 2025
- Collinear Superposition of SHMs · asked 2021, 2022, 2023, 2025
How it is asked
Difficulty, format and skill
Across all 57 questions on SHM Equations since 2017.
Difficulty
QUESTIONS- Easy30 · 53%
- Medium24 · 42%
- Hard3 · 5%
Format
SHARE- Single correct · 27 Q47%
- Numerical value · 21 Q37%
- Diagram based · 5 Q9%
- Other · 3 Q5%
- Match the list · 1 Q2%
Skill tested
SHARE- Calculation · 25 Q44%
- Application · 14 Q25%
- Multi-step · 10 Q18%
- Conceptual · 4 Q7%
- Data or graph · 4 Q7%
Repeats
New idea, or one asked before?
Each column is a year. Blue questions tested an idea no earlier year had asked; navy ones went back to an idea from an earlier year. 2017 is the first year, so everything in it counts as new. Heights are question counts, and Lumi analysed 1 to 24 shifts a year, so compare the split inside a column rather than heights across years.
- Idea asked for the first time
- Idea asked in an earlier year
Coverage of the topic
JEE Main has asked 21 of the 59 ideas in this topic. 32 have never been asked yet.
- Asked directly21 · 36%
- Touched inside another question6 · 10%
- Never asked32 · 54%
Ideas come from Lumi’s JEE syllabus map. A never-asked idea is not a safe skip: across all of JEE Main, 22% of questions since 2024 tested an idea no earlier year had asked.
Drill down
Chapter, idea, question
Every idea JEE Main tested in this topic, with its eight years. Open one to read the questions.
21 ideas inside
Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.
Ideas
Every idea inside this topic
21 different ideas were tested; 12 came more than once.
time period from v squared relation
Numerical value · 6 shifts · 5 numericalsuperposition of collinear shms
Numerical value · 6 shifts · 3 numericaltime between two positions in shm
Single correct · 4 shifts · 1 numericalcount correct statements on stacked-block shm
Numerical value · 5 shifts · 2 numericaltime period of mass between two springs
Diagram based · 5 shiftstime of zero velocity and acceleration in shm
Single correct · 4 shifts · 1 numericalperiod of mass on spring network
Numerical value · 4 shifts · 3 numericalinitial phase of shm from position and direction
Single correct · 4 shiftswavelength from wave equation and speed
Single correct · 3 shifts · 1 numericalmatch list on periodicity and shm of functions
Match the list · 2 shiftsmaximum velocity in shm
Numerical value · 2 shifts · 1 numericalgraph interpretation of velocity versus displacement in shm
Single correct · 2 shiftsfrequency ratio on cutting spring
Single correct · 1 shiftspring-mass frequency ratio for mass change
Numerical value · 1 shift · 1 numericalperiod from potential energy function
Numerical value · 1 shift · 1 numericalpath of particle from perpendicular shm components
Single correct · 1 shifttime between shm positions
Numerical value · 1 shift · 1 numericaltime for damped amplitude to halve
Single correct · 1 shiftgraph of velocity against displacement in shm
Single correct · 1 shifttorsional constant from time period
Single correct · 1 shiftfrequency of two-body spring oscillator
Numerical value · 1 shift · 1 numerical
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Velocity and Accel vs Positiontime period from v squared relation | 6 | 6 | Numerical valueCalculation | 5 | |
| Collinear Superposition of SHMssuperposition of collinear shms | 6 | 6 | Numerical valueCalculation | 3 | |
| Phasor Diagram Techniquetime between two positions in shm | 5 | 4 | Single correctApplication | 1 | |
| SHM Definition and Force Lawcount correct statements on stacked-block shm | 5 | 5 | Numerical valueCalculation | 2 | |
| Springs in Paralleltime period of mass between two springs | 5 | 5 | Diagram basedApplication | – | |
| Velocity and Accel vs Timetime of zero velocity and acceleration in shm | 4 | 4 | Single correctCalculation | 1 | |
| Springs in Seriesperiod of mass on spring network | 4 | 4 | Numerical valueApplication | 3 | |
| Phase and Initial Conditionsinitial phase of shm from position and direction | 4 | 4 | Single correctApplication | – | |
| General Solution of SHMwavelength from wave equation and speed | 3 | 3 | Single correctCalculation | 1 | |
| Non-SHM Periodic Functionsmatch list on periodicity and shm of functions | 2 | 2 | Match the listMulti-step | – | |
| Extrema of Kinematic and Energy Variablesmaximum velocity in shm | 2 | 2 | Numerical valueCalculation | 1 | |
| Velocity vs Position Graphgraph interpretation of velocity versus displacement in shm | 2 | 2 | Single correctData or graph | – | |
| Spring Cutting Rulefrequency ratio on cutting spring | 1 | 1 | Single correctApplication | – | |
| Standard Differential Equation Formspring-mass frequency ratio for mass change | 1 | 1 | Numerical valueCalculation | 1 | |
| Effective Spring Constant from Potential Energyperiod from potential energy function | 1 | 1 | Numerical valueCalculation | 1 | |
| Perpendicular Superposition (Lissajous)path of particle from perpendicular shm components | 1 | 1 | Single correctConceptual | – | |
| Standard Time Fractions in SHMtime between shm positions | 1 | 1 | Numerical valueCalculation | 1 | |
| Damped Amplitude Decaytime for damped amplitude to halve | 1 | 1 | Single correctCalculation | – | |
| Phase Space Trajectory (v vs x)graph of velocity against displacement in shm | 1 | 1 | Single correctData or graph | – | |
| Torsional Pendulum Time Periodtorsional constant from time period | 1 | 1 | Single correctCalculation | – | |
| Two-Body Oscillator Reduced Massfrequency of two-body spring oscillator | 1 | 1 | Numerical valueMulti-step | 1 |
Times and shifts count every analysed shift. Across JEE Main, 78% of questions since 2024 went back to an idea an earlier year had asked; the rest were new. All repeated ideas
Every question
SHM Equations questions, year by year
The newest 40 show their opening words as they appeared in the official paper; older ones name the idea they tested. Open one for its options and the official answer.
JEE Main 20265 questions in 5 shifts
- 2 Apr, Shift 2Q45The equation of motion of a particle is given by cm. The particle will come to rest at time…
Idea: Velocity and Accel vs Time
MediumSingle correct - 4 Apr, Shift 1Q48The velocity of a particle executing simple harmonic motion along -axis is described as , where represents…
Idea: Velocity and Accel vs Position
EasyNumerical value - 5 Apr, Shift 2Q35Match List - I with List - II. List - I A. B. C. D.…
Idea: Non-SHM Periodic Functions
HardMatch the list - 6 Apr, Shift 1Q37A particle is executing simple harmonic motion. Its amplitude is and time period is 5 sec. The time required by it to move from …
Idea: Phasor Diagram Technique
EasySingle correct - 8 Apr, Shift 2Q37The frequency of oscillation of a mass suspended by a spring is . If the length of the spring is cut to half, the same mass…
Idea: Spring Cutting Rule
New ideaEasySingle correct
JEE Main 20253 questions in 3 shifts
- 2 Apr, Shift 1Q33A particle is subjected to two simple harmonic motions as : cm and …
Idea: Collinear Superposition of SHMs
MediumSingle correct - 3 Apr, Shift 1Q36Two blocks of masses m and M, , are placed on a frictionless table as shown in figure. A massless spring with spring constant k…
Idea: SHM Definition and Force Law
Asked the year beforeHardOther · figure - 4 Apr, Shift 2Q34Displacement of a wave is expressed as m. The wavelength of the wave when its velocity is 300…
Idea: General Solution of SHM
EasySingle correct
JEE Main 20247 questions in 7 shifts
- 4 Apr, Shift 2Q56The displacement of a particle executing SHM is given by . The time period of motion is 3.14…
Idea: Velocity and Accel vs Time
EasyNumerical value - 6 Apr, Shift 1Q52A particle is doing simple harmonic motion of amplitude 0.06 m and time period 3.14 s. The maximum velocity of the particle is __________…
Idea: Extrema of Kinematic and Energy Variables
Asked the year beforeEasyNumerical value - 9 Apr, Shift 1Q54The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of m,…
Idea: Velocity and Accel vs Position
MediumNumerical value - 9 Apr, Shift 2Q57A particle of mass kg executes simple harmonic motion under force . The time period of oscillation is…
Idea: SHM Definition and Force Law
Asked the year beforeEasyNumerical value - 1 Feb, Shift 2Q54A mass is suspended from a spring of negligible mass and the system oscillates with a frequency . The frequency of oscillations…
Idea: Standard Differential Equation Form
New ideaEasyNumerical value - 31 Jan, Shift 1Q54A particle performs simple harmonic motion with amplitude . Its speed is increased to three times at an instant when its displacement…
Idea: Velocity and Accel vs Position
MediumNumerical value - 31 Jan, Shift 2Q54The time period of simple harmonic motion of mass in the given figure is , where the value of …
Idea: Springs in Series
MediumNumerical value · figure
JEE Main 20236 questions in 5 shifts
- 6 Apr, Shift 1Q43A mass m is attached to two strings as shown in figure. The spring constants of two springs are and . For the frictionless…
Idea: Springs in Parallel
Asked the year beforeEasyDiagram based · figure - 8 Apr, Shift 2Q32For particle revolving round the centre with radius of circular path and angular velocity , as shown in below figure,…
Idea: Phasor Diagram Technique
MediumSingle correct · figure - 10 Apr, Shift 1Q31A particle executes S.H.M. of amplitude A along -axis. At , the position of the particle is and it moves along…
Idea: Phase and Initial Conditions
Asked the year beforeEasySingle correct - 10 Apr, Shift 2Q32For a periodic motion represented by the equation the amplitude of the motion is
Idea: Collinear Superposition of SHMs
Asked the year beforeEasySingle correct - 10 Apr, Shift 2Q51A rectangular block of mass 5 kg attached to a horizontal spiral spring executes simple harmonic motion of amplitude 1 m and time period…
Idea: SHM Definition and Force Law
EasyNumerical value - 15 Apr, Shift 1Q31In a linear Simple Harmonic Motion (SHM) (A) Restoring force is directly proportional to the displacement. (B) The acceleration and…
Idea: Extrema of Kinematic and Energy Variables
New ideaEasyOther
JEE Main 202211 questions in 10 shifts
- 25 Jul, Shift 1Q39In figure (A), mass '2 m' is fixed on mass 'm' which is attached to two springs of spring constant k. In figure (B), mass 'm' is attached…
Idea: Springs in Parallel
Asked the year beforeMediumDiagram based · figure - 25 Jul, Shift 2Q57Two waves executing simple harmonic motions travelling in the same direction with same amplitude and frequency are superimposed. The…
Idea: Collinear Superposition of SHMs
Asked the year beforeEasyNumerical value - 26 Jul, Shift 1Q42When a particle executes Simple Hormonic Motion, the nature of graph of velocity as a function of displacement will be :
Idea: Velocity vs Position Graph
Asked the year beforeEasySingle correct - 26 Jul, Shift 2Q60As per given figures, two springs of spring constants and are connected to mass . If the period of oscillation in figure (a)…
Idea: Springs in Series
Asked the year beforeMediumNumerical value · figure - 28 Jul, Shift 2Q25The potential energy of a particle of mass 4 kg in motion along the -axis is given by U = 4(1 – cos 4) J. The time period of the…
Idea: Effective Spring Constant from Potential Energy
New ideaMediumNumerical value - 30 Jul, Shift 2Q26A particle executing SHM has its velocity 20 cm s at mean position and acceleration of 25 cm s at one of its extreme…
Idea: Velocity and Accel vs Position
Asked the year beforeMediumNumerical value - 24 Jun, Shift 2Q36Two massless springs with spring constants 2 k and 9 k, carry 50 g and 100 g masses at their free ends. These two masses oscillate…
Idea: Velocity and Accel vs Position
Asked the year beforeEasySingle correct - 27 Jun, Shift 1Q45The displacement of simple harmonic oscillator after 3 seconds starting from its mean position is equal to half of its amplitude. The time…
Idea: Phase and Initial Conditions
Asked the year beforeEasySingle correct - 27 Jun, Shift 2Q40The equation of a particle executing simple harmonic motion is given by m. At = 1s, the…
Idea: Velocity and Accel vs Time
EasySingle correct - 27 Jun, Shift 2Q54A particle executes simple harmonic motion. Its amplitude is 8 cm and time period is 6 s. The time it will take to travel from its…
Idea: Standard Time Fractions in SHM
New ideaMediumNumerical value - 28 Jun, Shift 1Q33Motion of a particle in - plane is described by a set of following equations m and…
Idea: Perpendicular Superposition (Lissajous)
New ideaEasySingle correct
JEE Main 202123 questions in 16 shifts
- 3 Aug, Shift 1Q9A sinusoidal wave is superposed on another periodic wave which is also oscillating with the same…
Idea: Collinear Superposition of SHMs
New ideaMediumSingle correct - 3 Aug, Shift 2Q1A particle is executing simple harmonic motion with time period . What is the time taken by the particle to go directly to…
Idea: Phasor Diagram Technique
New ideaEasySingle correct - 3 Aug, Shift 2Q2A block of mass m rigidly attached with a spring of spring constant , is compressed through a small distance A. If the block is now…
Idea: Phasor Diagram Technique
New ideaMediumSingle correct · figure - 3 Aug, Shift 2Q5One end of a metal wire is fixed at the centre of a uniform disc of radius 4.0 cm and mass 100 g. The other end of the wire is fixed with…
Idea: Torsional Pendulum Time Period
New ideaMediumSingle correct · figure - 4 Aug, Shift 1Q17If a particle of mass ‘m’ moves in x–y plane according to the equation (A sin314 t + B cos314 t) m The…
Idea: General Solution of SHM
New ideaEasySingle correct - 26 Aug, Shift 2Q24Two simple harmonic motions are represented by the equations and…
Idea: Collinear Superposition of SHMs
New ideaEasyNumerical value - 27 Aug, Shift 2Q27Two simple harmonic motion, are represented by the equations …
Idea: Collinear Superposition of SHMs
New ideaEasyNumerical value - 24 Feb, Shift 2Q7In the given figure, a body of mass M is held between two massless springs, on a smooth inclined plane. The free ends of the springs are…
Idea: Springs in Parallel
New ideaMediumDiagram based · figure - 24 Feb, Shift 2 · Q8Velocity vs Position GraphNew ideaEasy
- 25 Feb, Shift 2 · Q4SHM Definition and Force LawNew ideaMedium
- 25 Feb, Shift 2 · Q7Springs in ParallelNew ideaEasy
- 25 Feb, Shift 2 · Q8Phase and Initial ConditionsNew ideaMedium
- 26 Feb, Shift 1 · Q11Springs in SeriesNew ideaEasy
- 26 Feb, Shift 2 · Q16Phase Space Trajectory (v vs x)New ideaEasy
- 26 Feb, Shift 2 · Q22General Solution of SHMNew ideaMedium
- 26 Feb, Shift 2 · Q29Velocity and Accel vs PositionNew ideaEasy
- 22 Jul, Shift 2 · Q9Phase and Initial ConditionsNew ideaMedium
- 25 Jul, Shift 1 · Q22Two-Body Oscillator Reduced MassNew ideaMedium
- 16 Mar, Shift 2 · Q6Damped Amplitude DecayNew ideaMedium
- 17 Mar, Shift 1 · Q28Springs in SeriesNew ideaEasy
- 17 Mar, Shift 2 · Q6Springs in ParallelNew ideaEasy
- 18 Mar, Shift 1 · Q25Phasor Diagram TechniqueNew ideaMedium
- 18 Mar, Shift 2 · Q12SHM Definition and Force LawNew ideaMedium
JEE Main 20202 questions in 2 shifts
- 2 Sep, Shift 2 · Q2Velocity and Accel vs TimeNew ideaMedium
- 6 Sep, Shift 2 · Q10Non-SHM Periodic FunctionsNew ideaHard
Questions from the official JEE Main Paper 1 shifts published by NTA (CBSE for 2017). Questions NTA dropped are left out. Topic and idea tags, counts and notes are Lumi’s.