JEE Main Physics · Oscillations

SHM Equations in JEE Main

Name: SHM Equations: JEE Main previous year questions
Creator: Lumi

SHM Equations (Physics, Oscillations) came 22 times in 20 of the 42 JEE Main shifts Lumi analysed, across 13 distinct ideas. 12 of them came in 2024–26; it was last asked in 2026.

Questions: 22; in 20 shifts
Ideas asked: 13; 5 asked more than once
Numerical answer: 7; 32% of its questions
Pattern: Asked most years; last asked 2026

Questions each year

In the shifts Lumi analysed for each year.

Difficulty and format

Easy 7Medium 12Hard 3

Format

Single correct11 Q
Numerical value7 Q
Diagram based2 Q
Match the list1 Q
Other1 Q

Ideas inside the topic

13 ideas

Phasor Diagram Technique5 Q
Velocity and Accel vs Position3 Q
SHM Definition and Force Law2 Q
Non-SHM Periodic Functions2 Q
Springs in Parallel2 Q
Damped Amplitude Decay1 Q
General Solution of SHM1 Q
Spring Cutting Rule1 Q
Springs in Series1 Q
Collinear Superposition of SHMs1 Q
Torsional Pendulum Time Period1 Q
Two-Body Oscillator Reduced Mass1 Q

Where it sits

Part of Oscillations, which had 29 questions in all. SHM Equations accounts for 76% of them. In Lumi's JEE taxonomy it belongs to Waves and SHM.

Some questions sit in other chapters too: Waves.

Every question

All 22 SHM Equations questions

Newest first, each with its options and official answer.

2 Apr 2026, Shift 2 · Q45The equation of motion of a particle is given by $x = a\sin\left(50t + \frac{\pi}{3}\right)$ cm. The particle will come to rest at time…MediumSingle correct
4 Apr 2026, Shift 1 · Q48The velocity of a particle executing simple harmonic motion along $x$ -axis is described as $v^2=50-x^2$ , where $x$ represents…EasyNumerical value
5 Apr 2026, Shift 2 · Q35Match List - I with List - II. List - I A. $\sin^2\omega t$ B. $\sin^3(2\omega t)$ C. $\sin(\omega t)+\cos(\pi\omega t)$ D.…HardMatch the list
6 Apr 2026, Shift 1 · Q37A particle is executing simple harmonic motion. Its amplitude is $A$ and time period is 5 sec. The time required by it to move from $x=A$ …EasySingle correct
8 Apr 2026, Shift 2 · Q37The frequency of oscillation of a mass $m$ suspended by a spring is $v_1$ . If the length of the spring is cut to half, the same mass…EasySingle correct
2 Apr 2025, Shift 1 · Q33A particle is subjected to two simple harmonic motions as : $x_1=\sqrt{7}\sin5t$ cm and $x_2=2\sqrt{7}\sin\left(5t+\frac{\pi}{3}\right)$ …MediumSingle correct
3 Apr 2025, Shift 1 · Q36Two blocks of masses m and M, $(M > m)$ , are placed on a frictionless table as shown in figure. A massless spring with spring constant k…HardOtherHas a figure
4 Apr 2025, Shift 2 · Q34Displacement of a wave is expressed as $x(t)=5\cos\left(628t+\frac{\pi}{2}\right)$ m. The wavelength of the wave when its velocity is 300…EasySingle correct
9 Apr 2024, Shift 1 · Q54The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of $4$ m,…MediumNumerical value
9 Apr 2024, Shift 2 · Q57A particle of mass $0.50$ kg executes simple harmonic motion under force $F=-50\ (Nm^{-1})x$ . The time period of oscillation is…EasyNumerical value
31 Jan 2024, Shift 1 · Q54A particle performs simple harmonic motion with amplitude $A$ . Its speed is increased to three times at an instant when its displacement…MediumNumerical value
31 Jan 2024, Shift 2 · Q54The time period of simple harmonic motion of mass $M$ in the given figure is $\pi\sqrt{\frac{\alpha M}{5k}}$ , where the value of $\alpha$ …MediumNumerical valueHas a figure
6 Apr 2023, Shift 1 · Q43A mass m is attached to two strings as shown in figure. The spring constants of two springs are $K_1$ and $K_2$ . For the frictionless…EasyDiagram basedHas a figure
8 Apr 2023, Shift 2 · Q32For particle $P$ revolving round the centre $O$ with radius of circular path $r$ and angular velocity $\omega$ , as shown in below figure,…MediumSingle correctHas a figure
25 Jul 2022, Shift 1 · Q39In 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…MediumDiagram basedHas a figure
3 Aug 2021, Shift 2 · Q1A particle is executing simple harmonic motion with time period $T$ . What is the time taken by the particle to go directly to…EasySingle correct
3 Aug 2021, Shift 2 · Q2A block of mass m rigidly attached with a spring of spring constant $K$ , is compressed through a small distance A. If the block is now…MediumSingle correctHas a figure
3 Aug 2021, Shift 2 · Q5One 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…MediumSingle correctHas a figure
25 Jul 2021, Shift 1 · Q22In the reported figure, two bodies A and B of masses 200 g and 800 g are attached with the system of springs. Springs are kept in a…MediumNumerical valueHas a figure
16 Mar 2021, Shift 2 · Q6Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass = 500 g, Decay constant = 20 g/s…MediumSingle correct
18 Mar 2021, Shift 1 · Q25A particle performs simple harmonic motion with a period of 2 second. The time taken by the particle to cover a displacement equal to half…MediumNumerical value
6 Sep 2020, Shift 2 · Q10When a particle of mass m is attached to a vertical spring of spring constant k and released, its motion is described by…HardSingle correct